Bulletin of the Belgian Mathematical Society - Simon Stevin
- Bull. Belg. Math. Soc. Simon Stevin
- Volume 24, Number 4 (2017), 591-612.
An averaging formula for the coincidence Reidemeister trace
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.
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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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