Let \(f:M\to N\) be a map between two closed connected oriented manifolds. If \(f\) has degree 1, show that \(f_*:\pi _1(M)\to \pi _1(N)\) is an epimorphism.
Question
Math 6510 • Differentiable Manifolds
Winter 2005 • Question 3
Question
Winter 2005 • Question 3
Let \(f:M\to N\) be a map between two closed connected oriented manifolds. If \(f\) has degree 1, show that \(f_*:\pi _1(M)\to \pi _1(N)\) is an epimorphism.