differential geometry w notes from teacher_Part_103

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

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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 X p = 0 M p n X p = 0 B p . 3. Strong Morse inequalities M 0 B 0 M 1 - M 0 B
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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 geom.tex; April 12, 2006; 17:59; p. 203...
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This note was uploaded on 11/26/2011 for the course MAT 4821 taught by Professor Wong during the Spring '10 term at FSU.

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