## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Fixed point sets of equivariant fiber-preserving maps

#### Abstract

Given a selfmap $f:X\to X$ on a compact connected polyhedron $X$, H. Schirmer gave necessary and sufficient conditions for a nonempty closed subset $A$ to be the fixed point set of a map in the homotopy class of $f$. R. Brown and C. Soderlund extended Schirmer's result to the category of fiber bundles and fiber-preserving maps. The objective of this paper is to prove an equivariant analogue of Brown-Soderlund theorem result in the category of $G$-spaces and $G$-maps where $G$ is a finite group.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 24, Number 4 (2017), 641-655.

Dates
First available in Project Euclid: 4 January 2018

https://projecteuclid.org/euclid.bbms/1515035013

Digital Object Identifier
doi:10.36045/bbms/1515035013

Mathematical Reviews number (MathSciNet)
MR3743268

Zentralblatt MATH identifier
06848707

Subjects