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Chapter 7 Morse Theory and Floer Homology

Part of the Universitext book series (UTX)

Abstract

Let X be a complete Riemannian manifold, not necessarily of finite dimension.1 We shall consider a smooth function f on X, i.e. \({f}\,\epsilon\,{C}^{\propto}\,(X\,R)({\rm{actually}}\,{f}\,\epsilon\,\,{C}^{3})\,(X,\,{\mathbb{R}})\)usually suffices). The essential feature of the theory of Morse and its generalizations is the relationship between the structure of the critical set of f

Keywords

  • Unstable Manifold
  • Smale Condition
  • Fredholm Operator
  • Closed Geodesic
  • Morse Index

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  • DOI: 10.1007/978-3-642-21298-7_8
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Correspondence to Jürgen Jost .

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© 2011 Springer-Verlag Berlin Heidelberg

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Jost, J. (2011). Chapter 7 Morse Theory and Floer Homology. In: Riemannian Geometry and Geometric Analysis. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21298-7_8

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