Let \(M\) be a closed connected orientable 3-manifold with \(H_1(M;\mathbb {Z})=\mathbb {Z}\oplus \mathbb {Z}/2\mathbb {Z}\). Compute \(H_i(M;\mathbb {Z})\) and \(H^i(M;\mathbb {Z})\) for all \(i\).
Question
Math 6510 • Differentiable Manifolds
Spring 2013 • Question 10