Morse Theory

Amiya Mukherjee
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Amiya Mukherjee: Indian Statistical Institute, Statistics and Mathematics Unit

Chapter Chapter 9 in Differential Topology, 2015, pp 267-298 from Springer

Abstract: Abstract This chapter introduces Morse theory, which is of fundamental importance to differential topology. A Morse function $$f\;:\;M\;\rightarrow\;\mathbb{R}$$ is a smooth function having only simplest possible critical points, and in Morse theory one studies the relationship between the number of critical points of f and certain homological invariants of M such as Euler-Poincaré characteristic and Betti numbers.

Keywords: Simplicial Complex; Compact Manifold; Cell Complex; Betti Number; Homotopy Type (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-19045-7_9

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