Nielsen theory on infra-nilmanifolds modeled on the group of uni-triangular matrices


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	Nielsen theory on infra-nilmanifolds modeled on the group of uni-triangular matrices


	Fixed Point Theory, Volume 20, No. 2, 2019, 483-506, June 1st, 2019 DOI: 10.24193/fpt-ro.2019.2.31 Authors: Younggi Choi, Jong Bum Lee and Kyung Bai Lee Abstract: Let Nil_m be the group of m × m uni-triangular matrices. Then it is a connected and simply connected (m-1)-step nilpotent Lie group. Using the averaging formulas, we compute the spectra of the Lefschetz, Nielsen and Reidemeister (coincidence) numbers of maps on infra-nilmanifolds modeled on Nil_m. As a byproduct, we prove that the Bieberbach groups of Nil_m (m ≥ 4) with Γ_m as its nil-radical satisfy the R_∞ property. Key Words and Phrases: Averaging formula, infra-nilmanifold, Lefschetz number, Nielsen number, Reidemeister number, uni-triangular matrix. 2010 Mathematics Subject Classification: 57S30, 57S20, 22E25. Published on-line: June 1st, 2019. Abstract pdf Fulltext pdf Back to volume's table of contents