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Nielsen Theory on Nilmanifolds of the Standard Filiform Lie Group

  • Jong Bum LeeEmail author
  • Won Sok Yoo
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

Let M be a nilmanifold modeled on the standard filiform Lie group \(\mathcal {H}_{m+1}\) and let \(f:M\rightarrow M\) be a self-map. Using the averaging formulas, we compute the spectra of the Lefschetz, Nielsen, and Reidemeister (coincidence) numbers of maps f on M. Moreover, we give explicit formulas for a complete computation of the Nielsen type numbers \(N\mathrm {P}_n(f)\) and \(N\!\Phi _n(f)\). We also give a complete description of the sets of homotopy minimal periods of all such maps on M.

Keywords

Generalized Heisenberg group Homotopy minimal period Nielsen number Nielsen type number Nilmanifold 

2010 Mathematics Subject Classification

Primary: 55M20 Secondary: 57S30 

Notes

Acknowledgements

The authors would like to thank Karel Dekimpe for thorough reading, pointing out some errors, and valuable comments on the original version.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsSogang UniversitySeoulKorea
  2. 2.Department of Applied MathematicsKumoh National Institute of TechnologyKumiKorea

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