Equivalences for Morse homology

Matthias Schwarz

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Equivalences for Morse homology

Matthias Schwarz

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Abstract

An explicit isomorphism between Morse homology and singular homology is constructed via the technique of pseudo-cycles. Given a Morse cycle as a formal sum of critical points of a Morse function, the unstable manifolds for the negative gradient flow are compactified in a suitable way, such that gluing them appropriately leads to a pseudo-cycle and a well-defined integral homology class in singular homology.

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Matthias Schwarz. 1999-05-25. Equivalences for Morse homology. https://arxiv.org/abs/math/9905152

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