Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1998 • Question 7

Question

Math 6510 • Differentiable Manifolds Fall 1998 • Question 7

Let \(f:S^n\to S^n\) be a continuous map of spheres whose degree \(D(f)\ne 1\). Show that there is a point \(x\in S^n\) such that \(f(x)=a(x)\) where \(a\) is the antipodal map.

Raw LaTeX

Let \(f:S^n\to S^n\) be a continuous map of spheres whose degree \(D(f)\ne1\).
Show that there is a point \(x\in S^n\) such that \(f(x)=a(x)\) where \(a\) is the
antipodal map.

Topic Tags

Degree Theory Fixed Point Theorems and Borsuk-Ulam Homotopy and Degree on Manifolds