Actions of $2$-groups of bounded exponent on manifolds

TL;DR

This paper proves that infinite 2-groups with bounded exponent cannot have faithful smooth actions on compact manifolds, highlighting limitations on group actions in geometric topology.

Contribution

It establishes a new restriction on the actions of infinite 2-groups of bounded exponent on manifolds, a previously unexplored area.

Findings

Infinite 2-groups of bounded exponent cannot act faithfully and smoothly on compact manifolds.

The result constrains possible symmetries and group actions in geometric topology.

Provides insights into the structure and limitations of group actions on manifolds.

Abstract

In this paper, we show that an infinite 2-group of bounded exponent cannot act faithfully and smoothly on compact manifolds.