Equivariant Trees and Partition Complexes
Algebraic Topology
2026-02-04 v2 Combinatorics
Category Theory
Abstract
We introduce two definitions of -equivariant partitions of a finite -set, both of which yield -equivariant partition complexes. By considering suitable notions of equivariant trees, we show that -equivariant partitions and -trees are -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.
Cite
@article{arxiv.2302.08949,
title = {Equivariant Trees and Partition Complexes},
author = {Julia E. Bergner and Peter Bonventre and Maxine E. Calle and David Chan and Maru Sarazola},
journal= {arXiv preprint arXiv:2302.08949},
year = {2026}
}
Comments
Final version