English

Min-max theory for cell complexes

Algebraic Topology 2018-11-05 v1

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.

Keywords

Cite

@article{arxiv.1811.00719,
  title  = {Min-max theory for cell complexes},
  author = {Lacey Johnson and Kevin Knudson},
  journal= {arXiv preprint arXiv:1811.00719},
  year   = {2018}
}

Comments

10 pages, 2 figures

R2 v1 2026-06-23T05:01:40.740Z