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december 2017 An averaging formula for the coincidence Reidemeister trace
Jong Bum Lee, P. Christopher Staecker
Bull. Belg. Math. Soc. Simon Stevin 24(4): 591-612 (december 2017). DOI: 10.36045/bbms/1515035009

Abstract

In the setting of continuous maps between compact orientable manifolds of the same dimension, there is a well known averaging formula for the coincidence Lefschetz number in terms of the Lefschetz numbers of lifts to some finite covering space. We state and prove an analogous averaging formula for the coincidence Reidemeister trace. This generalizes a recent formula in fixed point theory by Liu and Zhao. We give two separate and independent proofs of our main result: one using methods developed by Kim and the first author for averaging Nielsen numbers, and one using an axiomatic approach for the local Reidemeister trace. We also give some examples and state some open questions for the nonorientable case.

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Jong Bum Lee. P. Christopher Staecker. "An averaging formula for the coincidence Reidemeister trace." Bull. Belg. Math. Soc. Simon Stevin 24 (4) 591 - 612, december 2017. https://doi.org/10.36045/bbms/1515035009

Information

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

zbMATH: 06848703
MathSciNet: MR3743264
Digital Object Identifier: 10.36045/bbms/1515035009

Subjects:
Primary: 54H25, ‎55M20

Rights: Copyright © 2017 The Belgian Mathematical Society

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Vol.24 • No. 4 • december 2017
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