People_

Professor Stephan Tillmann

School of Mathematics &
Statistics
Professor of Geometric Topology

Phone

9351 2005

Fax

9351 4534

Email

stephan.tillmann@sydney.edu.au

Address

F07 - Carslaw Building

The University of Sydney

Websites

Personal web page

Biographical details

2002 PhD (The University of Melbourne)

Research interests

Stephan Tillmann is a member of the Geometry, Topology and Analysis Research Group. Stephan's main research interests are geometry and topology with a focus on low-dimensional manifolds. He uses techniques from algebraic geometry, hyperbolic and projective geometry, geometric group theory, representations of finitely generated groups, differential geometry as well as tropical geometry. A principal aim of his current research is to understand the relationship between triangulations of, geometric structures on, and surfaces in 3-manifolds with view towards new topological results about 3-manifolds, practical algorithms, and applications to group theory.

Teaching and supervision

Timetable

Current research students

Project title	Research student
Complexity of 3-Manifolds	James MORGAN

Publications

By Type

Expand all

Book Chapters

Rubinstein, H., Spreer, J., Tillmann, S. (2024). A New Family of Minimal Ideal Triangulations of Cusped Hyperbolic 3–manifolds. In David R Wood, Jan de Gier, Cheryl Praeger (Eds.), 2021-2022 Matrix Annals (Matrix Book #5), (pp. 5-24). Switzerland: Springer. [More Information]
Spreer, J., Tillmann, S. (2018). Unravelling the Dodecahedral Spaces. In Jan de Gier, Cheryl E. Praeger, Terence Tao (Eds.), 2016 MATRIX Annals, (pp. 323-347). Cham: Springer International Publishing. [More Information]

Journals

Jaco, W., Rubinstein, H., Spreer, J., Tillmann, S. (2025). Complexity of 3-manifolds obtained by Dehn filling. Algebraic and Geometric Topology, 25(1), 301-327. [More Information]
Jaco, W., Rubinstein, H., Spreer, J., Tillmann, S. (2024). Slope norm and an algorithm to compute the crosscap number. Algebraic and Geometric Topology, 24(8), 4307-4351. [More Information]
Spreer, J., Tillmann, S. (2022). Determining the trisection genus of orientable and non-orientable PL 4-manifolds through triangulations. Experimental Mathematics, 31(3), 897-907. [More Information]
Porti, J., Tillmann, S. (2021). Projective Structures on a Hyperbolic 3-orbifold. Acta Mathematica Vietnamica, 46(2), 347-355. [More Information]
Casella, A., Katerba, C., Tillmann, S. (2020). Ideal points of character varieties, algebraic non-integral representations, and undetected closed essential surfaces in 3–manifolds. Proceedings of the American Mathematical Society, 148(5), 2257-2271. [More Information]
Rubinstein, H., Tillmann, S. (2020). Multisections of Piecewise Linear Manifolds. Indiana University Mathematics Journal, 69(6), 2209-2239. [More Information]
Jaco, W., Rubinstein, H., Spreer, J., Tillmann, S. (2020). On minimal ideal triangulations of cusped hyperbolic 3-manifolds. Journal of Topology, 13(1), 308-342. [More Information]
Friedl, S., Tillmann, S. (2020). Two-generator one-relator groups and marked polytopes. Annales de l'Institut Fourier, 70(2), 831-879. [More Information]
Jaco, W., Rubinstein, H., Spreer, J., Tillmann, S. (2020). Z2 –thurston norm and complexity of 3–manifolds, II. Algebraic and Geometric Topology, 20(1), 503-529. [More Information]
Chu, M., Tillmann, S. (2019). Reflections on trisection genus. Revue Roumaine de Mathematiques Pures et Appliquees, 64(4), 395-402.
Haraway, R., Tillmann, S. (2019). Tessellating the Moduli Space of Strictly Convex Projective Structures on the Once-Punctured Torus. Experimental Mathematics, 28(3), 369-384. [More Information]
Rubinstein, H., Segerman, H., Tillmann, S. (2019). Traversing three-manifold triangulations and spines. L'Enseignement Mathematique, 65(2), 155-206. [More Information]
Bell, M., Hass, J., Rubinstein, H., Tillmann, S. (2018). Computing trisections of 4-manifolds. Proceedings of the National Academy of Sciences of the United States of America, 115(43), 10901-10907. [More Information]
Cooper, D., Long, D., Tillmann, S. (2018). Deforming convex projective manifolds. Geometry and Topology, 22(3), 1349-1404. [More Information]
Rubinstein, H., Tillmann, S. (2018). Generalized trisections in all dimensions. Proceedings of the National Academy of Sciences of the United States of America, 115(43), 10908-10913. [More Information]
Friedl, S., Gill, M., Tillmann, S. (2018). Linear representations of 3–manifold groups over rings. Proceedings of the American Mathematical Society, 146(11), 4951-4966. [More Information]
Luo, F., Tillmann, S. (2017). A new combinatorial class of 3-manifold triangulations. The Asian Journal of Mathematics, 21(3), 543-570. [More Information]
Casella, A., Luo, F., Tillmann, S. (2017). Pseudo-developing maps for ideal triangulations II: Positively oriented ideal triangulations of cone-manifolds. Proceedings of the American Mathematical Society, 145(8), 3543-3560. [More Information]
Friedl, S., Schreve, K., Tillmann, S. (2017). Thurston norm via Fox calculus. Geometry and Topology, 21(6), 3759-3784. [More Information]
Klaff, B., Tillmann, S. (2016). A birationality result for character varieties. Mathematical Research Letters, 23(4), 1099-1110. [More Information]
Jaco, W., Johnson, J., Spreer, J., Tillmann, S. (2016). Bounds for the genus of a normal surface. Geometry and Topology, 20(3), 1625-1671. [More Information]
Cooper, D., Tillmann, S. (2015). Complexity functions on 1-dimensional cohomology. Revue Roumaine de Mathematiques Pures et Appliquees, 60(4), 535-550.
Rubinstein, H., Tillmann, S. (2015). Even triangulations of n-dimensional pseudo-manifolds. Algebraic and Geometric Topology, 15(5), 2949-2984. [More Information]
Cooper, D., Long, D., Tillmann, S. (2015). On convex projective manifolds and cusps. Advances in Mathematics, 277, 181-251. [More Information]
Luo, F., Tillmann, S., Yang, T. (2013). Thurston's spinning construction and solutions to the hyperbolic gluing equations for closed hyperbolic 3-manifolds. Proceedings of the American Mathematical Society, 141(1), 335-350. [More Information]
Tillmann, S. (2012). Degenerations of ideal hyperbolic triangulations. Mathematische Zeitschrift, 272(3-4), 793-823. [More Information]
Burton, B., Rubinstein, H., Tillmann, S. (2012). The Weber-Seifert dodecahedral space is non-haken. Transactions of the American Mathematical Society, 364(2), 911-932. [More Information]
Jaco, W., Rubinstein, H., Tillmann, S. (2011). Coverings and minimal triangulations of 3-manifolds. Algebraic and Geometric Topology, 11(3), 1257-1265. [More Information]
Tillmann, S. (2011). Geometry and Topology Down Under. Gazette of the Australian Mathematical Society, 38(5), 261-263.
Hodgson, C., Rubinstein, H., Segerman, H., Tillmann, S. (2011). Veering triangulations admit strict angle structures. Geometry and Topology, 15(4), 2073-2089. [More Information]
Jaco, W., Rubinstein, H., Tillmann, S. (2009). Minimal triangulations for an infinite family of lens spaces. Journal of Topology, 2(1), 157-180. [More Information]
Cooper, D., Tillmann, S. (2009). The Thurston norm via normal surfaces. Pacific Journal of Mathematics, 239(1), 1-15. [More Information]
Luo, F., Tillmann, S. (2008). Angle structures and normal surfaces. Transactions of the American Mathematical Society, 360(6), 2849-2866. [More Information]
Luo, F., Schleimer, S., Tillmann, S. (2008). Geodesic ideal triangulations exist virtually. Proceedings of the American Mathematical Society, 136(7), 2625-2630. [More Information]
Tillmann, S. (2008). Normal surfaces in topologically finite 3-manifolds. L'Enseignement Mathematique, 54(2), 329-380.
Chesebro, E., Tillmann, S. (2007). Not all boundary slopes are strongly detected by the character variety. Communications in Analysis and Geometry, 15(4), 695-723.
Tillmann, S. (2005). Boundary slopes and the logarithmic limit set. Topology, 44(1), 203-216.
Tillmann, S. (2004). Character varieties of mutative 3â€“manifolds. Algebraic and Geometric Topology, 4, 133-149.
Tillmann, S. (2000). On the Kinoshita-Terasaka knot and generalised Conway mutation. Journal of Knot Theory and Its Ramifications, 9(4), 557-575. [More Information]

show 36 more

Conferences

Friedl,, S., Lück,, W., Tillmann, S. (2019). Groups and polytopes. Proceedings of Symposia in Pure Mathematics, : IEEE Computer Society.
Spreer, J., Tillmann, S. (2018). The trisection genus of standard simply connected PL 4-manifolds. 34th Annual Symposium on Computational Geometry (SoCG 2018), Germany: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. [More Information]
Chang, H., Erickson, J., Letscher, D., de Mesmay, A., Schleimer, S., Sedgwick, E., Thurston, D., Tillmann, S. (2018). Tightening Curves on Surfaces via Local Moves. The Twenty-Ninth Annual ACM/SIAM Symposium on Discrete Algorithms (SODA 2018), USA: Society for Industrial and Applied Mathematics (SIAM). [More Information]
Burton, B., Coward, A., Tillmann, S. (2013). Computing Closed Essential Surfaces in Knot Complements. SoCG 13 The twenty-ninth annual symposium on Computational geometry 2013, New York: Association for Computing Machinery (ACM). [More Information]
Tillmann, S. (2012). Structure of 0â€“efficient or minimal triangulations. Triangulations Workshop, Zurich: EMS Publishing House.
Segerman, H., Tillmann, S. (2011). Pseudo-Developing Maps for Ideal Triangulations I: Essential Edges and Generalised Hyperbolic Gluing Equations. Topology and Geometry in Dimension Three: Triangulations, Invariants, and Geometric Structures, Stillwater, OK, USA: Oklahoma State University. [More Information]

show 3 more

By Year

Expand all

2025

Jaco, W., Rubinstein, H., Spreer, J., Tillmann, S. (2025). Complexity of 3-manifolds obtained by Dehn filling. Algebraic and Geometric Topology, 25(1), 301-327. [More Information]

2024

Rubinstein, H., Spreer, J., Tillmann, S. (2024). A New Family of Minimal Ideal Triangulations of Cusped Hyperbolic 3–manifolds. In David R Wood, Jan de Gier, Cheryl Praeger (Eds.), 2021-2022 Matrix Annals (Matrix Book #5), (pp. 5-24). Switzerland: Springer. [More Information]
Jaco, W., Rubinstein, H., Spreer, J., Tillmann, S. (2024). Slope norm and an algorithm to compute the crosscap number. Algebraic and Geometric Topology, 24(8), 4307-4351. [More Information]

2022

Spreer, J., Tillmann, S. (2022). Determining the trisection genus of orientable and non-orientable PL 4-manifolds through triangulations. Experimental Mathematics, 31(3), 897-907. [More Information]

2021

Porti, J., Tillmann, S. (2021). Projective Structures on a Hyperbolic 3-orbifold. Acta Mathematica Vietnamica, 46(2), 347-355. [More Information]

2020

Casella, A., Katerba, C., Tillmann, S. (2020). Ideal points of character varieties, algebraic non-integral representations, and undetected closed essential surfaces in 3–manifolds. Proceedings of the American Mathematical Society, 148(5), 2257-2271. [More Information]
Rubinstein, H., Tillmann, S. (2020). Multisections of Piecewise Linear Manifolds. Indiana University Mathematics Journal, 69(6), 2209-2239. [More Information]
Jaco, W., Rubinstein, H., Spreer, J., Tillmann, S. (2020). On minimal ideal triangulations of cusped hyperbolic 3-manifolds. Journal of Topology, 13(1), 308-342. [More Information]
Friedl, S., Tillmann, S. (2020). Two-generator one-relator groups and marked polytopes. Annales de l'Institut Fourier, 70(2), 831-879. [More Information]
Jaco, W., Rubinstein, H., Spreer, J., Tillmann, S. (2020). Z2 –thurston norm and complexity of 3–manifolds, II. Algebraic and Geometric Topology, 20(1), 503-529. [More Information]

show 2 more

2019

Friedl,, S., Lück,, W., Tillmann, S. (2019). Groups and polytopes. Proceedings of Symposia in Pure Mathematics, : IEEE Computer Society.
Chu, M., Tillmann, S. (2019). Reflections on trisection genus. Revue Roumaine de Mathematiques Pures et Appliquees, 64(4), 395-402.
Haraway, R., Tillmann, S. (2019). Tessellating the Moduli Space of Strictly Convex Projective Structures on the Once-Punctured Torus. Experimental Mathematics, 28(3), 369-384. [More Information]
Rubinstein, H., Segerman, H., Tillmann, S. (2019). Traversing three-manifold triangulations and spines. L'Enseignement Mathematique, 65(2), 155-206. [More Information]

show 1 more

2018

Bell, M., Hass, J., Rubinstein, H., Tillmann, S. (2018). Computing trisections of 4-manifolds. Proceedings of the National Academy of Sciences of the United States of America, 115(43), 10901-10907. [More Information]
Cooper, D., Long, D., Tillmann, S. (2018). Deforming convex projective manifolds. Geometry and Topology, 22(3), 1349-1404. [More Information]
Rubinstein, H., Tillmann, S. (2018). Generalized trisections in all dimensions. Proceedings of the National Academy of Sciences of the United States of America, 115(43), 10908-10913. [More Information]
Friedl, S., Gill, M., Tillmann, S. (2018). Linear representations of 3–manifold groups over rings. Proceedings of the American Mathematical Society, 146(11), 4951-4966. [More Information]
Spreer, J., Tillmann, S. (2018). The trisection genus of standard simply connected PL 4-manifolds. 34th Annual Symposium on Computational Geometry (SoCG 2018), Germany: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. [More Information]
Chang, H., Erickson, J., Letscher, D., de Mesmay, A., Schleimer, S., Sedgwick, E., Thurston, D., Tillmann, S. (2018). Tightening Curves on Surfaces via Local Moves. The Twenty-Ninth Annual ACM/SIAM Symposium on Discrete Algorithms (SODA 2018), USA: Society for Industrial and Applied Mathematics (SIAM). [More Information]
Spreer, J., Tillmann, S. (2018). Unravelling the Dodecahedral Spaces. In Jan de Gier, Cheryl E. Praeger, Terence Tao (Eds.), 2016 MATRIX Annals, (pp. 323-347). Cham: Springer International Publishing. [More Information]

show 4 more

2017

Luo, F., Tillmann, S. (2017). A new combinatorial class of 3-manifold triangulations. The Asian Journal of Mathematics, 21(3), 543-570. [More Information]
Casella, A., Luo, F., Tillmann, S. (2017). Pseudo-developing maps for ideal triangulations II: Positively oriented ideal triangulations of cone-manifolds. Proceedings of the American Mathematical Society, 145(8), 3543-3560. [More Information]
Friedl, S., Schreve, K., Tillmann, S. (2017). Thurston norm via Fox calculus. Geometry and Topology, 21(6), 3759-3784. [More Information]

2016

Klaff, B., Tillmann, S. (2016). A birationality result for character varieties. Mathematical Research Letters, 23(4), 1099-1110. [More Information]
Jaco, W., Johnson, J., Spreer, J., Tillmann, S. (2016). Bounds for the genus of a normal surface. Geometry and Topology, 20(3), 1625-1671. [More Information]

2015

Cooper, D., Tillmann, S. (2015). Complexity functions on 1-dimensional cohomology. Revue Roumaine de Mathematiques Pures et Appliquees, 60(4), 535-550.
Rubinstein, H., Tillmann, S. (2015). Even triangulations of n-dimensional pseudo-manifolds. Algebraic and Geometric Topology, 15(5), 2949-2984. [More Information]
Cooper, D., Long, D., Tillmann, S. (2015). On convex projective manifolds and cusps. Advances in Mathematics, 277, 181-251. [More Information]

2013

Burton, B., Coward, A., Tillmann, S. (2013). Computing Closed Essential Surfaces in Knot Complements. SoCG 13 The twenty-ninth annual symposium on Computational geometry 2013, New York: Association for Computing Machinery (ACM). [More Information]
Luo, F., Tillmann, S., Yang, T. (2013). Thurston's spinning construction and solutions to the hyperbolic gluing equations for closed hyperbolic 3-manifolds. Proceedings of the American Mathematical Society, 141(1), 335-350. [More Information]

2012

Tillmann, S. (2012). Degenerations of ideal hyperbolic triangulations. Mathematische Zeitschrift, 272(3-4), 793-823. [More Information]
Tillmann, S. (2012). Structure of 0â€“efficient or minimal triangulations. Triangulations Workshop, Zurich: EMS Publishing House.
Burton, B., Rubinstein, H., Tillmann, S. (2012). The Weber-Seifert dodecahedral space is non-haken. Transactions of the American Mathematical Society, 364(2), 911-932. [More Information]

2011

Jaco, W., Rubinstein, H., Tillmann, S. (2011). Coverings and minimal triangulations of 3-manifolds. Algebraic and Geometric Topology, 11(3), 1257-1265. [More Information]
Tillmann, S. (2011). Geometry and Topology Down Under. Gazette of the Australian Mathematical Society, 38(5), 261-263.
Segerman, H., Tillmann, S. (2011). Pseudo-Developing Maps for Ideal Triangulations I: Essential Edges and Generalised Hyperbolic Gluing Equations. Topology and Geometry in Dimension Three: Triangulations, Invariants, and Geometric Structures, Stillwater, OK, USA: Oklahoma State University. [More Information]
Hodgson, C., Rubinstein, H., Segerman, H., Tillmann, S. (2011). Veering triangulations admit strict angle structures. Geometry and Topology, 15(4), 2073-2089. [More Information]

show 1 more

2009

Jaco, W., Rubinstein, H., Tillmann, S. (2009). Minimal triangulations for an infinite family of lens spaces. Journal of Topology, 2(1), 157-180. [More Information]
Cooper, D., Tillmann, S. (2009). The Thurston norm via normal surfaces. Pacific Journal of Mathematics, 239(1), 1-15. [More Information]

2008

Luo, F., Tillmann, S. (2008). Angle structures and normal surfaces. Transactions of the American Mathematical Society, 360(6), 2849-2866. [More Information]
Luo, F., Schleimer, S., Tillmann, S. (2008). Geodesic ideal triangulations exist virtually. Proceedings of the American Mathematical Society, 136(7), 2625-2630. [More Information]
Tillmann, S. (2008). Normal surfaces in topologically finite 3-manifolds. L'Enseignement Mathematique, 54(2), 329-380.

2007

Chesebro, E., Tillmann, S. (2007). Not all boundary slopes are strongly detected by the character variety. Communications in Analysis and Geometry, 15(4), 695-723.

2005

Tillmann, S. (2005). Boundary slopes and the logarithmic limit set. Topology, 44(1), 203-216.

2004

Tillmann, S. (2004). Character varieties of mutative 3â€“manifolds. Algebraic and Geometric Topology, 4, 133-149.

2000

Tillmann, S. (2000). On the Kinoshita-Terasaka knot and generalised Conway mutation. Journal of Knot Theory and Its Ramifications, 9(4), 557-575. [More Information]

Selected Grants

2019

Trisections, triangulations and the complexity of manifolds, Tillmann S, Rubinstein H, Spreer J, Australian Research Council (ARC)/Discovery Projects (DP)

2018

To support the establishment of SUMRI (Syd Uni Math Research Institute), Tillmann S, DVC Research/Other

2017

Interactions between geometric and topological structures, Tillmann S, Australian Research Council (ARC)/Future Fellowships (FT)

2015

Invariants, geometric and discrete structures on manifolds, Rubinstein H, Tillmann S, Hodgson C, Australian Research Council (ARC)/Discovery Projects (DP)

2014

Moduli spaces of geometric structures, Tillmann S, Australian Research Council (ARC)/Discovery Projects (DP)

2012

Triangulations in dimensions 3 and 4: discrete and geometric structures, Rubinstein H, Hodgson C, Tillmann S, Australian Research Council (ARC)/Discovery Projects (DP)

2010

Generic complexity in computational topology: breaking through the bottlenecks, Burton B, Elder M, Tillmann S, Australian Research Council (ARC)/Discovery Projects (DP)

2009

Triangulations in dimension three: algorithms and geometric structures, Rubinstein H, Tillmann S, Hodgson C, Australian Research Council (ARC)/Discovery Projects (DP)

Faculty of Science

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