- #1
pp31
- 10
- 0
Suppose a Morse function [tex]f:S^n\rightarrow R[/tex] satisfies f(x) = f(-x). Show that f must have atleast 2 critical points of index j for all j = 0,...,n.
Show that any MOrse function on a compact set of genus g has at least 2g+2 critical points.
These are the questions and I have no idea how to get started. If some one could just push me in the right direction I would really appreciate it.
Show that any MOrse function on a compact set of genus g has at least 2g+2 critical points.
These are the questions and I have no idea how to get started. If some one could just push me in the right direction I would really appreciate it.