Smooth nondisplaceability for fixed point sets of involutions

TL;DR

This paper proves that on closed manifolds with odd Euler characteristic, the fixed point sets of involutions cannot be smoothly displaced, highlighting a topological rigidity property.

Contribution

It establishes a new smooth nondisplaceability result for fixed point sets of involutions on certain manifolds.

Findings

Fixed point sets are smoothly nondisplaceable on manifolds with odd Euler characteristic.

The result applies to closed manifolds, emphasizing topological constraints.

Provides insight into symmetry actions and fixed point theory.

Abstract

We prove that on closed manifolds of odd Euler characteristic fixed point sets of involutions are smoothly nondisplaceable.