Let \(M\) be a closed, orientable manifold of dimension \(2k\) and assume that \(H_{k-1}(M,\mathbb {Z})\) is torsion-free. Show that \(H_k(M,\mathbb {Z})\) is torsion free.
Question
Math 6510 • Differentiable Manifolds
Fall 2016 • Question 11
Question
Fall 2016 • Question 11
Let \(M\) be a closed, orientable manifold of dimension \(2k\) and assume that \(H_{k-1}(M,\mathbb {Z})\) is torsion-free. Show that \(H_k(M,\mathbb {Z})\) is torsion free.