Fixed point sets of equivariant fiber-preserving maps

zbMATH Open1390.55004arXiv1704.01413MaRDI QIDQ1704379

Peng Zhang

Publication date: 9 March 2018

Published in: Bulletin of the Belgian Mathematical Society - Simon Stevin (Search for Journal in Brave)

Abstract: Given a selfmap $f:XoX$ 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.

Full work available at URL: https://arxiv.org/abs/1704.01413

zbMATH Keywords

triangulationfixed pointsequivariant mapssmooth manifoldssmooth mapsfibre maps

Mathematics Subject Classification ID

Compact Lie groups of differentiable transformations (57S15) Finite transformation groups (57S17) Fixed points and coincidences in algebraic topology (55M20) Fiber bundles in algebraic topology (55R10)

Related Items (2)

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