Cup products and the higher topological complexity of configuration spaces of the circle with two anchored points

2022/12/01 by Hoekstra-Mendoza, Teresa I.
#55M30 #55N45 #57Q70 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.00220

Abstract

In this paper we show how to compute cup products in the anchored configuration space of the circle with two anchored points using discrete Morse theory. Knowing how to compute cup products allows us to obtain bounds for the (higher) topological complexity TC_s, which are sharp for a sufficiently large value of s.

Related

• The symmetrized topological complexity of the circle
• Topological complexity of configuration spaces
• On topological complexity of twisted products
• The higher topological complexity of subcomplexes of products of spheres---and related polyhedral product spaces
• Min-type Morse theory for configuration spaces of hard spheres