On the Level Set of a Function with Degenerate Minimum Point

Yasuhiko Kamiyama

International Journal of Mathematics and Mathematical Sciences, 2015, vol. 2015, 1-6

Abstract:

For , let be an -dimensional smooth closed manifold and a smooth function. We set and assume that is attained by unique point such that is a nondegenerate critical point. Then the Morse lemma tells us that if is slightly bigger than , is diffeomorphic to . In this paper, we relax the condition on from being nondegenerate to being an isolated critical point and obtain the same consequence. Some application to the topology of polygon spaces is also included.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:493217

DOI: 10.1155/2015/493217

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