Min-Max Theory for Cell Complexes

• 作者: Lacey Johnson Kevin Knudson
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2020,（3）
• 页码范围: 447-454
• 页数: 8页
• 语种: 英文
• DOI: 10.1142/S100538672000036X

摘要

In the study of smooth functions on manifolds,min-max theory provides a mechanism for identifying critical values of a function.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.