The homotopy fixed point sets of spheres actions on rational complexes

TL;DR

This paper investigates the homotopy types of fixed point sets under sphere group actions on rational spaces, providing new descriptions and properties relevant to algebraic topology.

Contribution

It offers a detailed description of homotopy fixed point sets for $S^3$-actions on rational spheres and projective spaces, and explores properties of $S^1$-actions on rational complexes.

Findings

Homotopy fixed point sets of $S^3$-actions on rational spheres characterized.

Properties of $S^1$-actions on rational complexes established.

New descriptions of fixed point sets in algebraic topology context.

Abstract

In this paper, we describe the homotopy type of the homotopy fixed point sets of $S^3$-actions on rational spheres and complex projective spaces, and provide some properties of $S^1$-actions on a general rational complex.