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december 2017 Stabilizers of fixed point classes and Nielsen numbers of $n$-valued maps
Robert F. Brown, Junzheng Nan
Bull. Belg. Math. Soc. Simon Stevin 24(4): 523-535 (december 2017). DOI: 10.36045/bbms/1515035005

Abstract

The stabilizer of a fixed point class of a map is the fixed subgroup of the induced fundamental group homomorphism based at a point in the class. A theorem of Jiang, Wang and Zhang is used to prove that if a map of a graph satisfies a strong remnant condition, then the stabilizers of all its fixed point classes are trivial. Consequently, if $\phi_{p, f}$ is the $n$-valued lift to a covering space $p$ of a map $f$ with strong remnant of a graph, then the Nielsen numbers are related by the equation $N(\phi_{p, f}) = n \cdot N(f)$. Additional information concerning Nielsen numbers is obtained for $n$-valued lifts of maps of graphs with positive Lefschetz numbers and of maps of spaces with abelian fundamental groups and for extensions of $n$-valued maps.

Citation

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Robert F. Brown. Junzheng Nan. "Stabilizers of fixed point classes and Nielsen numbers of $n$-valued maps." Bull. Belg. Math. Soc. Simon Stevin 24 (4) 523 - 535, december 2017. https://doi.org/10.36045/bbms/1515035005

Information

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

zbMATH: 06848699
MathSciNet: MR3743260
Digital Object Identifier: 10.36045/bbms/1515035005

Subjects:
Primary: ‎54C60‎, ‎55M20

Rights: Copyright © 2017 The Belgian Mathematical Society

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Vol.24 • No. 4 • december 2017
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