Computing Reidemeister classes

Davide Ferrario

Fundamenta Mathematicae (1998)

  • Volume: 158, Issue: 1, page 1-18
  • ISSN: 0016-2736

Abstract

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In order to compute the Nielsen number N(f) of a self-map f: X → X, some Reidemeister classes in the fundamental group π 1 ( X ) need to be distinguished. In this paper some algebraic results are given which allow distinguishing Reidemeister classes and hence computing the Reidemeister number of some maps. Examples of computations are presented.

How to cite

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Ferrario, Davide. "Computing Reidemeister classes." Fundamenta Mathematicae 158.1 (1998): 1-18. <http://eudml.org/doc/212299>.

@article{Ferrario1998,
abstract = {In order to compute the Nielsen number N(f) of a self-map f: X → X, some Reidemeister classes in the fundamental group $π_1(X)$ need to be distinguished. In this paper some algebraic results are given which allow distinguishing Reidemeister classes and hence computing the Reidemeister number of some maps. Examples of computations are presented.},
author = {Ferrario, Davide},
journal = {Fundamenta Mathematicae},
keywords = {Reidemeister numbers; fixed point theory; Nielsen numbers},
language = {eng},
number = {1},
pages = {1-18},
title = {Computing Reidemeister classes},
url = {http://eudml.org/doc/212299},
volume = {158},
year = {1998},
}

TY - JOUR
AU - Ferrario, Davide
TI - Computing Reidemeister classes
JO - Fundamenta Mathematicae
PY - 1998
VL - 158
IS - 1
SP - 1
EP - 18
AB - In order to compute the Nielsen number N(f) of a self-map f: X → X, some Reidemeister classes in the fundamental group $π_1(X)$ need to be distinguished. In this paper some algebraic results are given which allow distinguishing Reidemeister classes and hence computing the Reidemeister number of some maps. Examples of computations are presented.
LA - eng
KW - Reidemeister numbers; fixed point theory; Nielsen numbers
UR - http://eudml.org/doc/212299
ER -

References

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  1. [B] R. F. Brown, The Lefschetz Fixed Point Theorem, Scott and Foresman, 1971. Zbl0216.19601
  2. [DHT] O. Davey, E. Hart and K. Trapp, Computation of Nielsen numbers for maps of closed surfaces, Trans. Amer. Math. Soc. 348 (1996), 3245-3266. Zbl0861.55003
  3. [FaHu] E. Fadell and S. Husseini, The Nielsen number on surfaces, in: Contemp. Math. 21, Amer. Math. Soc., 1983, 59-98. Zbl0563.55001
  4. [FeHi] A. Fel'shtyn and R. Hill, The Reidemeister zeta function with applications to Nielsen theory and a connection with Reidemeister torsion, K-Theory 8 (1994), 367-393. 
  5. [Ha] B. Halpern, Periodic points on the Klein bottle, manuscript. 
  6. [He] P. R. Heath, Product formulae for Nielsen numbers of fibre maps, Pacific J. Math. 117 (1985), 267-289. Zbl0571.55002
  7. [HKW] P. R. Heath, E. Keppelmann and P. N. S. Wong, Addition formulae for Nielsen numbers and Nielsen-type numbers of fibre preserving maps, Topology Appl. 67 (1995), 133-157. Zbl0845.55004
  8. [Hu] S. Y. Husseini, Generalized Lefschetz numbers, Trans. Amer. Math. Soc. 272 (1982), 247-274. Zbl0507.55001
  9. [J] B. J. Jiang, Lectures on Nielsen Fixed Point Theory, Contemp. Math. 14, Amer. Math. Soc., Providence, 1983. Zbl0512.55003
  10. [MKS] W. Magnus, A. Karrass and D. Solitar, Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations, Dover, 1966. Zbl0138.25604
  11. [McC] C. K. McCord, Computing Nielsen numbers, in: Nielsen Theory and Dynamical Systems (South Hadley, Mass., 1992), Contemp. Math. 152, Amer. Math. Soc., Providence, 1993, 249-267. 
  12. [W] P. Wong, Fixed-point theory for homogeneous spaces, Amer. J. Math. 120 (1998), 23-42. Zbl0908.55002
  13. [Y] C. Y. You, Fixed point classes of a fiber map, Pacific J. Math. 100 (1982), 217-241. Zbl0512.55004

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