An application of topological equivalence to Morse theory

Details An application of topological equivalence to Morse theory An application of topological equivalence to Morse theory

2011-02-14

arxiv.org/abs/1102.2838v1

Mathematics

Geometric Topology

Scientific paper

In a previous paper, under the assumption that the Riemannian metric is special, the author proved some results about the moduli spaces and CW structures arising from Morse theory. By virtue of topological equivalence, this paper extends those results by dropping the assumption on the metric. In particular, we give a strong solution to the following classical question: Does a Morse function on a compact Riemannian manifold gives rise to a CW decomposition that is homeomorphic to the manifold?

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