Abstract
The main goal of this chapter is to show how to construct a CW-complex that is homotopy equivalent to a given smooth manifold M using some special functions on M called “Morse” functions (Theorem 3.28). The CW-homology of the resulting CW-complex is isomorphic to the singular homology of M by Theorem 2.15, and hence it is independent of the choice of the Morse function used to build the CW-complex. As a consequence we derive the Morse inequalities. The last section of this chapter is an introduction to Morse-Bott functions.
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© 2004 Springer Science+Business Media Dordrecht
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Banyaga, A., Hurtubise, D. (2004). Basic Morse Theory. In: Lectures on Morse Homology. Kluwer Texts in the Mathematical Sciences, vol 29. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2696-6_3
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DOI: https://doi.org/10.1007/978-1-4020-2696-6_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6705-0
Online ISBN: 978-1-4020-2696-6
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