# Computing Reidemeister classes

Fundamenta Mathematicae (1998)

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

## Access Full Article

top## Abstract

top## How to cite

topFerrario, 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

top- [B] R. F. Brown, The Lefschetz Fixed Point Theorem, Scott and Foresman, 1971. Zbl0216.19601
- [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
- [FaHu] E. Fadell and S. Husseini, The Nielsen number on surfaces, in: Contemp. Math. 21, Amer. Math. Soc., 1983, 59-98. Zbl0563.55001
- [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.
- [Ha] B. Halpern, Periodic points on the Klein bottle, manuscript.
- [He] P. R. Heath, Product formulae for Nielsen numbers of fibre maps, Pacific J. Math. 117 (1985), 267-289. Zbl0571.55002
- [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
- [Hu] S. Y. Husseini, Generalized Lefschetz numbers, Trans. Amer. Math. Soc. 272 (1982), 247-274. Zbl0507.55001
- [J] B. J. Jiang, Lectures on Nielsen Fixed Point Theory, Contemp. Math. 14, Amer. Math. Soc., Providence, 1983. Zbl0512.55003
- [MKS] W. Magnus, A. Karrass and D. Solitar, Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations, Dover, 1966. Zbl0138.25604
- [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.
- [W] P. Wong, Fixed-point theory for homogeneous spaces, Amer. J. Math. 120 (1998), 23-42. Zbl0908.55002
- [Y] C. Y. You, Fixed point classes of a fiber map, Pacific J. Math. 100 (1982), 217-241. Zbl0512.55004

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.