NDLI: Fixed point sets of fiber-preserving maps

Content Provider	Springer Nature Link
Author	Brown, Robert F. Soderlund, Christina L.
Copyright Year	2007
Abstract	Let $$\mathfrak{F} = (E, p, B; Y)$$ be a fiber bundle where E, B and Y are connected finite polyhedra. Let $$f : E \longrightarrow E$$ be a fiber-preserving map and $$A \subseteq E$$ a closed, locally contractible subset. We present necessary and sufficient conditions for A and its subsets to be the fixed point sets of maps fiber homotopic to f. The necessary conditions correspond to those introduced by Schirmer in 1990 but, in the fiber-preserving setting, homotopies are fiberpreserving. Those conditions are shown to be sufficient in the presence of additional hypotheses on the bundle and on the map f. The hypotheses can be weakened in the case that f is fiber homotopic to the identity.
Starting Page	41
Ending Page	53
Page Count	13
File Format	PDF
ISSN	16617738
Journal	Journal of Fixed Point Theory and Applications
Volume Number	2
Issue Number	1
e-ISSN	16617746
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	2007-07-14
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Fiber-preserving map fiber deformation Fixed points and coincidences Fiber bundles Mathematics Analysis Mathematical Methods in Physics
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology Applied Mathematics Modeling and Simulation

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Fixed point sets of fiber-preserving maps