Bulletin of the Belgian Mathematical Society - Simon Stevin

Fixed point index bounds for self-maps on closed surfaces

D.L. Gonçalves and M.R. Kelly

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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.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 24, Number 4 (2017), 673-688.

Dates
First available in Project Euclid: 4 January 2018

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1515035016

Digital Object Identifier
doi:10.36045/bbms/1515035016

Mathematical Reviews number (MathSciNet)
MR3743271

Zentralblatt MATH identifier
06848710

Subjects
Primary: 55M20: Fixed points and coincidences [See also 54H25] 54H25: Fixed-point and coincidence theorems [See also 47H10, 55M20] 57M99: None of the above, but in this section 37B30: Index theory, Morse-Conley indices

Keywords
fixed point index surface minimal map

Citation

Gonçalves, D.L.; Kelly, M.R. Fixed point index bounds for self-maps on closed surfaces. Bull. Belg. Math. Soc. Simon Stevin 24 (2017), no. 4, 673--688. doi:10.36045/bbms/1515035016. https://projecteuclid.org/euclid.bbms/1515035016


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