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REIDEMEISTER ORBIT SETS ON THE MAPPING TORUS
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 Title & Authors
REIDEMEISTER ORBIT SETS ON THE MAPPING TORUS
Lee, Seoung-Ho;
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 Abstract
The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. Let f : G G be an endomorphism between the fundamental group of the mapping torus. Extending Jiang and Ferrario's works on Reidemeister sets, we obtain algebraic results such as addition formulae for Reidemeister orbit sets of f relative to Reidemeister sets on suspension groups. In particular, if f is an automorphism, an similar formula for Reidemeister orbit sets of f relative to Reidemeister sets on given groups is also proved.
 Keywords
Reidemeister sets;Reidemeister orbit sets;suspension groups;
 Language
English
 Cited by
 References
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2.
D. Ferrario, Computing Reidemeister classes, Fund. Math. 158 (1998), 1-18.

3.
P. R. Heath, Product formula for Nielsen numbers of fibre maps, Pacific J. Math. 117 (1985), 267-289. crossref(new window)

4.
B. Jiang, Lectures on Nielsen Fixed Point Theory, vol. 14, Contemp. Math., 1983.

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B. Jiang, A characterization of fixed point classes, in: Fixed Point Theory and its applications (R. F. Brown, ed.), Contemp. Math. 72 (1988), 157-160.

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B. Jiang, S. H. Lee and M. H. Woo, Reidemeister orbit sets, to appear.

7.
R. C. Lyndon and P. E. Schupp, Combinatorial Group Theory, Springer, Berlin- Heidelberg-New York, 1977.