A stronger reformulation of Webb's conjecture in terms of finite topological spaces

TL;DR

This paper proposes a stronger version of Webb's conjecture related to the topology of finite spaces and proves specific cases using fusion theory and homotopy theory.

Contribution

It introduces a new, stronger conjecture reformulating Webb's conjecture in terms of finite topological spaces and proves particular cases.

Findings

Proposes a stronger reformulation of Webb's conjecture.

Proves specific cases using fusion and homotopy theories.

Connects group theory with finite topological space topology.

Abstract

We investigate a stronger formulation of Webb's conjecture on the contractibilty of the orbit space of the p-subgroup complexes in terms of finite topological spaces. The original conjecture, which was first proved by Symonds and, more recently, by Bux, Libman and Linckelmann, can be restated in terms of the topology of certain finite spaces. We propose a stronger conjecture, and prove various particular cases by combining fusion theory of finite groups and homotopy theory of finite spaces.