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.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Morse function on a sphere

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