[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2006.21.1.193

A RELATIVE REIDEMEISTER ORBIT NUMBER

Lee, Seoung-Ho (Mokwon University)
Yoon, Yeon-Soo (Hannam University)

Publication Information

Communications of the Korean Mathematical Society / v.21, no.1, 2006 , pp. 193-209 More about this Journal

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. In this paper, extending Cardona and Wong's work on relative Reidemeister numbers, we show that the Reidemeister orbit numbers can be used to calculate the relative essential orbit numbers. We also apply the relative Reidemeister orbit number to study periodic orbits of fibre preserving maps.

Keywords

Reidemeister sets; relative Reidemeister orbit numbers; Nielsen type relative essential n-orbit numbers;

Citations & Related Records

Reference

1	R. F. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresman and Co., Glenview, IL, 1971
2	F. Cardona and P. Wong, On the computation of the relative Nielsen number, Topology Appl. 116 (2001), 29-41 DOI ScienceOn
3	F. Cardona and P. Wong, The relative Reidemeister numbers of fiber map pairs, Topological Methods in Nonlinear Analysis Journal of the Juliusz Schauder Center 21 (2003), 131-145 DOI
4	P. R. Heath, R. Piccinini and C. You, Nielsen type numbers for periodic points on nonconnected spaces, Topology Appl. 63 (1995), 97-116 DOI ScienceOn
5	P. R. Heath, R. Piccinini and C. You, Nielsen type numbers for periodic points on pairs of spaces, Topology Appl. 63 (1995), 117-138 DOI ScienceOn
6	B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemporary Mathematics 14 (AMS, Providence, RI 1983)
7	B. Jiang, S. H. Lee and M. H. Woo, Reidemeister orbit sets, Fund. Math. 183 (2004), 139-156 DOI
8	H. Schirmer, A relative Nielsen number, Paciffic J. Math. 122 (1986), 459-473 DOI
9	E. Spanier, Algebraic Topology, McGraw-Hill, New York 1966
10	P. Wong, Fixed point theory for homogeneous spaces, Amer. J. Math. 120 (1998), 23-42 DOI
11	C. You, Fixed Point Classes of a Fibre Map, Paciffic J. Math. 100 (1992), no. 1, 217-241
12	X. Zhao, A relative Nielsen number for the complement, in: Topological Fixed Point Theory and Applications, Proceedings, (Tianjin 1988), B. Jiang (ed.), Lecture Notes in Math. 1411, Springer, Berlin 1989, 189-199
13	P. R. Heath, R. Piccinini and C. You, Nielsen-type numbers for periodic points I, in: Topological Fixed Point Theory and Applications, Proceedings, (Tianjin 1988), B. Jiang (ed.), Lecture Notes in Math. 1411, Springer, Berlin 1989, 88- 106
14	P. R. Heath, A Nielsen type number for fibre preserving maps, Topology and Appl. 53 (1993), 19-35 DOI ScienceOn
15	P. R. Heath and E. C. Keppelmann, Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds II, Topology and Appl. 106 (2000), 149-167 DOI ScienceOn