Let \(M\) be a closed, orientable manifold \(M\) of dimension \(2k\). If \(H_{k-1}(M)\) is torsion free show that \(H_k(M)\) is torsion free.
Question
Math 6510 • Differentiable Manifolds
Winter 2005 • Question 18
Question
Winter 2005 • Question 18
Let \(M\) be a closed, orientable manifold \(M\) of dimension \(2k\). If \(H_{k-1}(M)\) is torsion free show that \(H_k(M)\) is torsion free.