S4. If M is a closed orientable 3-manifold then it is Z-homology cobordant to a3-manifold which is Haken and hyperbolic [Liv81, My83]. ... presentations. Abelianizing P1 = ⟨a1,. , an | r1,. , rn⟩ determines an n nintegral matrix C which is a
S4. If M is a closed orientable 3-manifold then it is Z-homology cobordant to a3-manifold which is Haken and hyperbolic [Liv81, My83]. ... presentations. Abelianizing P1 = ⟨a1,. , an | r1,. , rn⟩ determines an n nintegral matrix C which is a
Proposition 5.1. Suppose an nn matrix A can be written in block diagonal formA = B C, then eA = eBeC. ... eBeC. Okay, so we can now apply Proposition 5.1 to Λ and get that eΛ = eΛ1 eΛ2 , andlikewise eΛt = eΛ1t eΛ2t.