2018/11/02 by Johnson, Lacey, Knudson, Kevin
#57Q10 #Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1811.00719
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.