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MORSE THEORY J. Milnor BY Based on lecture notes by M. SPIVAK and R. WELLS PRINCETON, NEW JERSEY PRINCETON UNIVERSITY PRESS 1963
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- 3.1 Morse homology modulo 2
- ! 0 ! Cn(h; Z=2Z) = Z=2Z ! 0 ! ! 0 ! C0(h; Z=2Z) = Z=2Z ! 0 ! :
- Ftj[0;1=3] f0; Ftj[2=3;1] f1:
- Let mk
- t : C (M; Z) ! C (M; Z);
In the rst chapter we established that given a compact manifold, Morse functions exist and are generic. In the second chapter we established moreover that pairs (f; X) where f is Morse and X is a pseudo-gradient adapted to f satisfying the Smale condition exist and are generic. Such (f; X) are said to be Morse-Smale. Let M be a compact manifold, an...
Each boundary map is necessarily the zero-map, forcing the Morse homologies to be
We call such an F an end-constant interpolation. Let EndConstInt(M) denote the cate-gory of Morse-Smale pairs on M, where morphisms between Morse-Smale pairs are equiv-alence classes of end-constant interpolations. (Two end-constant interpolations are equiva-lent if they take the same constant values, i.e. if they have the same domain and codomain....
mk bk(M): This is the weak version of the discrete Morse inequality. This doesn't quite follow from our proof that the Morse and cellular homologies of a manifold are equal, as we have not shown that every cellular decomposition induces a suitable Morse-Smale pair. As a corollary, it follows that there are no cellular decompositions of a torus into...
tk : Ck(M; Z) ! Cn k(M; Z): In particular, for each k there is an isomorphism Hk(M; Z) = Hn k(M; Z). First we must make sense of cohomology in the sense of Morse complexes. In singular homology, the chain complex is directly dualised to give singular cohomology. That is, each Ck is replaced with C = HomR(Ck; R), and the boundary maps are replaced w...
One of the most cited books in mathematics, John Milnor’s exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse.
Mar 2, 2016 · One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the...
Mar 2, 2016 · One of the most cited books in mathematics, John Milnor’s exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse.
One of the most cited books in mathemat-ics, John Milnor’s expo-sition of Morse theory has been the most impor-tant book on the subject for more than forty years. Morse theory was devel-oped in the s by math-ematician Marston Morse.
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xml. One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse.
