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december 2017 Fixed point index bounds for self-maps on closed surfaces
D.L. Gonçalves, M.R. Kelly
Bull. Belg. Math. Soc. Simon Stevin 24(4): 673-688 (december 2017). DOI: 10.36045/bbms/1515035016

Abstract

Given a surface with non-positive Euler characteristic and non-empty boundary, and a map which has the least number of fixed points possible within its homotopy class there are known bounds (both upper and lower) regarding the fixed point indices of the map. This paper gives a new proof of this result. In addition, a relative version of the method is developed, which is then used to establish the same index bounds for the case of a closed surface of negative Euler characteristic.

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D.L. Gonçalves. M.R. Kelly. "Fixed point index bounds for self-maps on closed surfaces." Bull. Belg. Math. Soc. Simon Stevin 24 (4) 673 - 688, december 2017. https://doi.org/10.36045/bbms/1515035016

Information

Published: december 2017
First available in Project Euclid: 4 January 2018

zbMATH: 06848710
MathSciNet: MR3743271
Digital Object Identifier: 10.36045/bbms/1515035016

Subjects:
Primary: 37B30, 54H25, ‎55M20, 57M99

Rights: Copyright © 2017 The Belgian Mathematical Society

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Vol.24 • No. 4 • december 2017
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