Let \(f:M\to N\) be a map of degree 1 between two smooth, closed, connected, oriented \(n\)-manifolds. Prove that \(f_*:\pi _1(M)\to \pi _1(N)\) is surjective.
Question
Math 6510 • Differentiable Manifolds
Winter 2007 • Question 11
Question
Winter 2007 • Question 11
Let \(f:M\to N\) be a map of degree 1 between two smooth, closed, connected, oriented \(n\)-manifolds. Prove that \(f_*:\pi _1(M)\to \pi _1(N)\) is surjective.