Show that if a closed orientable manifold \(M\) of dimension \(2k\) has \(H_{k-1}(M;\mathbb {Z})\) torsionfree, then \(H_k(M;\mathbb {Z})\) is also torsionfree.
Question
Math 6510 • Differentiable Manifolds
Fall 2006 • Question 15
Question
Fall 2006 • Question 15
Show that if a closed orientable manifold \(M\) of dimension \(2k\) has \(H_{k-1}(M;\mathbb {Z})\) torsionfree, then \(H_k(M;\mathbb {Z})\) is also torsionfree.