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Morse Theory for Geodesics in Conical Manifolds

Authors
  • Ghimenti, Marco G.
Type
Published Article
Publication Date
Dec 26, 2010
Submission Date
Dec 26, 2010
Identifiers
arXiv ID: 1012.5520
Source
arXiv
License
Yellow
External links

Abstract

The aim of this paper is to extend the Morse theory for geodesics to the conical manifolds. We define these manifolds as submanifolds of $\R^n$ with a finite number of conical singularities. To formulate a good Morse theory we must use an appropriate definition of geodesic. The main theorem of this paper claims that, although the energy is nonsmooth, we can find a continuous retraction of its sublevels in absence of critical points. So, we can give a good definition of index for isolated critical values and for isolated critical points. We prove that Morse relations hold and, at last, we give a definition of multiplicity of geodesics which is geometrical meaningful.

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