Manifolds with the fixed point property and their squares

TL;DR

This paper investigates the fixed point property in manifolds and their Cartesian squares, providing examples where the property does not extend to symmetric squares, highlighting limitations in fixed point behavior.

Contribution

It constructs examples of manifolds with the fixed point property whose symmetric squares lack this property, revealing new insights into fixed point phenomena.

Findings

Symmetric squares of certain manifolds can fail to have the fixed point property.

Examples demonstrate the non-preservation of the fixed point property under symmetric square operations.

The study advances understanding of fixed point behavior in manifold products.

Abstract

The Cartesian squares (powers) of manifolds with the fixed point property (f.p.p.) are considered. Examples of manifolds with the f.p.p. are constructed whose symmetric squares fail to have the f.p.p..