Min-max theory for cell complexes

Lacey Johnson; Kevin Knudson

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arXiv · 1811.00719

Min-max theory for cell complexes

Lacey Johnson·Kevin Knudson

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Abstract

In the study of smooth functions on manifolds, min-max theory provides a mechanism for identifying critical values of a function. In this paper we introduce a discretized version of this theory associated to a discrete Morse function on a (regular) cell complex. As applications we prove a discrete version of the Mountain Pass Lemma and give an alternate proof of a discrete Lusternik-Schnirelmann Theorem.

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BibTeX RIS

Lacey Johnson, Kevin Knudson. 2018-11-02. Min-max theory for cell complexes. https://arxiv.org/abs/1811.00719

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