Bulletin of the Belgian Mathematical Society - Simon Stevin

Fixed point sets of equivariant fiber-preserving maps

Rafael Souza and Peter Wong

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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

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1515035013

Digital Object Identifier
doi:10.36045/bbms/1515035013

Mathematical Reviews number (MathSciNet)
MR3743268

Zentralblatt MATH identifier
06848707

Subjects
Primary: 55M20: Fixed points and coincidences [See also 54H25]
Secondary: 57S99: None of the above, but in this section

Keywords
fixed points equivariant maps

Citation

Souza, Rafael; Wong, Peter. Fixed point sets of equivariant fiber-preserving maps. Bull. Belg. Math. Soc. Simon Stevin 24 (2017), no. 4, 641--655. doi:10.36045/bbms/1515035013. https://projecteuclid.org/euclid.bbms/1515035013


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