Witten’s Proof of Morse Inequalities
نویسنده
چکیده
Both properties do not depend on the choice of coordinates. The index ind (x) is the number of negative eigenvalues of Hess (f) (x). Let mp = mp (f) be the number of critical points of index p. Let bp = bp (M) = dimH (M) be the dimension of the p de Rham cohomology group. 0→ Ω (M) d −→ Ω (M) d −→ ... d −→ Ω (M) d −→ 0 This is called the de Rham complex. Note that d = 0. If ω = dα, then dω = 0. So Imd : Ωp−1 → Ω ⊆ ker d : Ω → Ω, and
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