Bulletin of the Belgian Mathematical Society - Simon Stevin

An averaging formula for the coincidence Reidemeister trace

Jong Bum Lee and P. Christopher Staecker

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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.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 24, Number 4 (2017), 591-612.

First available in Project Euclid: 4 January 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 54H25: Fixed-point and coincidence theorems [See also 47H10, 55M20] 55M20: Fixed points and coincidences [See also 54H25]

Averaging formula coincidence point fixed point Nielsen theory Reidemeister trace


Lee, Jong Bum; Staecker, P. Christopher. An averaging formula for the coincidence Reidemeister trace. Bull. Belg. Math. Soc. Simon Stevin 24 (2017), no. 4, 591--612. doi:10.36045/bbms/1515035009. https://projecteuclid.org/euclid.bbms/1515035009

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