REIDEMEISTER ZETA FUNCTION FOR GROUP EXTENSIONS

  • Wong, Peter (Department of mathematics Bates College)
  • Published : 2001.11.01

Abstract

In this paper, we study the rationality of the Reidemeister zeta function of an endomorphism of a group extension. As an application, we give sufficient conditions for the rationality of the Reidemeister and the Nielsen zeta functions of selfmaps on an exponential solvmanifold or an infra-nilmanifold or the coset space of a compact connected Lie group by a finite subgroup.

Keywords

References

  1. Ann. Math. v.81 On periodic points M. Artin;B. Mazur
  2. Memoirs Amer. Math. Soc. v.699 Dynamical zeta functions, Nielsen theory and Reidemeister torsion A. Fel'shtyn
  3. Springer LNM v.1346 New zeta funtions for dynamical systems and Nielsen fixed point theory A. Fel'shtyn
  4. Colloq. Math. v.62 The Reidemeister zeta functions and the computation of the Nielsen zeta function A. Fel'shtyn
  5. Forum Math. v.10 Trace formulae, zeta functions, congruences and Reidemeister torsion in Nielsen theory A. Fel'shtyn;R. Hill
  6. Topo. Appl. v.67 Reidemeister numbers of equivariant maps A. Fel'shtyn;R. Hill;P. Wong
  7. Top. Appl. v.83 Coincidence Reidemeister classes on nilmanifolds and nilpotent fibrations D. Goncalves
  8. Amer. Math. Soc. v.14 Lectures on Nielsen Fixed Point Theory, Contemporary Mathematics B. Jiang
  9. Periodic points on Klein bottle (unpublished) B. Halpern
  10. Topo. Appl. v.67 Addition formulae for Nielsen numbers and for Nielsen type numbers of fiber-preserving maps P. Heath. E. Keppelmann;P. Wong
  11. Homogeneous spaces in coincidence theory, Ⅱ (preprint) D. Goncalves;P. Wong
  12. Pacific J. Math. v.170 The Anosov theorem for exponential solvmanifolds E. Keppelmann;C. McCord
  13. Pacific J. Math. v.168 Maps on infra-nilmanifolds K. B. Lee
  14. Bull. Amer. Math. Soc. v.73 Differentiable dynamical systems S. Smale
  15. Amer. J. Math. v.120 Fixed point theory for homogeneous spaces P. Wong