Let \(M\) be a closed, orientable manifold of dimension \(2k\) and assume that \(H_{k-1}(M)\) is torsion free. Show that \(H_k(M)\) is torsion free.
Question
Math 6510 • Differentiable Manifolds
Fall 2008 • Question 12
Question
Fall 2008 • Question 12
Let \(M\) be a closed, orientable manifold of dimension \(2k\) and assume that \(H_{k-1}(M)\) is torsion free. Show that \(H_k(M)\) is torsion free.