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Topological method for detecting fixed points of maps homotopic to selfmaps of compact ENRs


Authors: Grzegorz Kosiorowski and Klaudiusz Wójcik
Journal: Proc. Amer. Math. Soc. 141 (2013), 245-252
MSC (2000): Primary 37C25, 58J20; Secondary 32S50
DOI: https://doi.org/10.1090/S0002-9939-2012-11295-X
Published electronically: May 9, 2012
MathSciNet review: 2988726
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Abstract: Assume that $ X$ is a metric space and $ B\subset X$ is compact. Let $ f:B\to X$ be a continuous map homotopic to $ g$, the selfmap of $ B$. The aim of this paper is to present a method for detecting fixed points of $ f$. It is based on the notion of the Ważewski set for the homotopy $ F$ between $ g$ and $ f$.


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Additional Information

Grzegorz Kosiorowski
Affiliation: Instytut Matematyki Uniwersytetu Jagiellońskiego, ul. Stanisława Łojasiewicza 6, 30-348 Kraków, Poland
Address at time of publication: Katedra Matematyki Uniwersytetu Ekonomicznego w Krakowie, ul. Rakowicka 27, 31-520 Kraków, Poland
Email: Grzegorz.Kosiorowski@gmail.com, Grzegorz.Kosiorowski@uek.krakow.pl

Klaudiusz Wójcik
Affiliation: Instytut Matematyki Uniwersytetu Jagiellońskiego, ul. Stanisława Łojasiewicza 6, 30-348 Kraków, Poland

DOI: https://doi.org/10.1090/S0002-9939-2012-11295-X
Keywords: Lefschetz number, relative Nielsen number, fixed point index
Received by editor(s): November 1, 2010
Received by editor(s) in revised form: June 3, 2011, and June 9, 2011
Published electronically: May 9, 2012
Additional Notes: This work was co-financed with budget funds allocated to education in 2010-2011 as a research project by the grant N N201 411439.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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