Equivariant Trees and Partition Complexes

2023/02/17 by Bergner, Julia E., Bonventre, Peter, Calle, Maxine E. +2
#05A18 #05E18 #20E08 #55P91 #Algebraic Topology (math.AT) #Category Theory (math.CT) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.08949

Abstract

We introduce two definitions of G-equivariant partitions of a finite G-set, both of which yield G-equivariant partition complexes. By considering suitable notions of equivariant trees, we show that G-equivariant partitions and G-trees are G-homotopy equivalent, generalizing existing results for the non-equivariant setting. Along the way, we develop equivariant versions of Quillen's Theorems A and B, which are of independent interest.

Related

• A comparison of definitions of equivariant trees
• Partition complexes and trees
• Equivariant Γ-spaces
• Computing Equivariant Homotopy with a Splitting Method
• Generalizing a partition theorem of Andrews