Let \(\Sigma \) be a closed, smooth surface. Show that if \(\Sigma \) admits a nonvanishing vector field, then the Euler characteristic of \(\Sigma \) equals 0.
Question
Math 6510 • Differentiable Manifolds
Fall 2017 • Question 6
Question
Fall 2017 • Question 6
Let \(\Sigma \) be a closed, smooth surface. Show that if \(\Sigma \) admits a nonvanishing vector field, then the Euler characteristic of \(\Sigma \) equals 0.