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Nielsen coincidence theory on infra-solvmanifolds of Sol

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Abstract

We derive averaging formulas for the Lefschetz coincidence numbers, the Nielsen coincidence numbers and the Reidemeister coincidence numbers of maps on infra-solvmanifolds modeled on a connected and simply connected solvable Lie group of type (R). As an application, we compare our formula for the Nielsen coincidence numbers with a result of Jezierski (1992) for pairs of maps on some infra-solvmanifolds of Sol. For all pairs of self-maps of a nonorientable infra-solvmanifold of Sol, we determine the sets of all possible values of the Nielsen coincidence numbers and the Reidemeister coincidence numbers.

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Acknowledgements

The first author was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education (Grant No. NRF-2016R1D1A1B01006971). The authors thank the referees for their thorough reading and helpful comments, in particular on Proposition 6.1 (see Proposition 6.3 and Remark 6.4) in the original version of the article.

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Authors and Affiliations

  1. Department of Mathematics, Sogang University, Seoul, 121-742, Korea

    Jong Bum Lee

  2. Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, SP, 13565-905, Brazil

    Karen Regina Panzarin

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  1. Jong Bum Lee
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  2. Karen Regina Panzarin
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Correspondence to Jong Bum Lee.

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Lee, J.B., Panzarin, K.R. Nielsen coincidence theory on infra-solvmanifolds of Sol. Sci. China Math. 64, 1861–1884 (2021). https://doi.org/10.1007/s11425-020-1767-x

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  • DOI: https://doi.org/10.1007/s11425-020-1767-x

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