Morse homology on noncompact manifolds

Kai Cieliebak; Urs Frauenfelder

doi:10.4134/JKMS.2011.48.4.749

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2011; 48(4): 749-774

Printed July 1, 2011

https://doi.org/10.4134/JKMS.2011.48.4.749

Morse homology on noncompact manifolds

Kai Cieliebak and Urs Frauenfelder

Ludwig-Maximilians-Universit\"at, Seoul National University

Abstract

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Abstract

Given a Morse function on a manifold whose moduli spaces of gradient flow lines for each action window are compact up to breaking one gets a bidirect system of chain complexes. There are different possibilities to take limits of such a bidirect system. We discuss in this note the relation between these different limits.

Keywords: Morse homology, bidirect system, direct and inverse limits

MSC numbers: 53D40