{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

differential geometry w notes from teacher_Part_103

differential geometry w notes from teacher_Part_103 - 1-B M...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
7.6. RELATIVE HOMOLOGY AND MORSE THEORY 205 Corollary 7.6.1 There hold: 1. Weak Morse inequalities M p B p , 2. In particular, the total number of critical points is bounded below by the sum of all Betti numbers n p = 0 M p n p = 0 B p . 3. Strong Morse inequalities M 0 B 0 M
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1-B . . . M n-M n-1 + ··· + (-1) n M = B n-B n-1 + ··· + (-1) n B . 4. In particular, n X p = (-1) p M p = n X p = (-1) p B p Proof : 1. ± di ff geom.tex; April 12, 2006; 17:59; p. 203...
View Full Document

{[ snackBarMessage ]}