Simplicial and combinatorial versions of higher symmetric topological complexity

2021/04/07 by Paul, Amit Kumar, Sen, Debasis
#05E45 #06A07 #57Q05 #68T40 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.03038

Abstract

In this paper, we introduce higher symmetric simplicial complexity SC_n^Σ(K) of a simplicial complex K and higher symmetric combinatorial complexity CC_n^Σ(P) of a finite poset P. These are simplicial and combinatorial approaches to symmetric motion planning of Basabe - González - Rudyak - Tamaki. We prove that the symmetric simplicial complexity SC_n^Σ(K) is equal to symmetric topological complexity TC_n^Σ(|K|) of the geometric realization of K and the symmetric combinatorial complexity CC_n^Σ(P) is equal to symmetric topological complexity TC_n^Σ(|K(P)|) of the geometric realization of the order complex of P.

Related

• Higher analogs of simplicial and combinatorial complexity
• Symmetric Motion Planning
• Bidirectional Sequential Motion Planning
• A Finite Equivariant Generalization of Motion Planning and Topological Complexity
• On higher analogs of topological complexity