On the number of stabilizer subgroups in a finite group acting on a manifold

TL;DR

This paper establishes a bound on the number of stabilizer subgroups for finite p-group actions on compact manifolds, which is key to proving a significant conjecture in the field.

Contribution

It introduces a bound depending only on the manifold for the number of stabilizer subgroups in finite p-group actions, aiding in the proof of Ghys' conjecture.

Findings

Existence of a universal bound C for stabilizer subgroups

Identification of a subgroup H with bounded index where the action has limited stabilizers

Application to the proof of Ghys' conjecture

Abstract

If a finite p-group G acts continuously on a compact topological manifold M then, with some bound C depending on M alone, G has a subgroup H of index at most C such that the H-action on M has at most C stabilizer subgroups. This result plays a crucial role in the proof of a deep conjecture of Ghys.