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A NIELSEN TYPE NUMBER OF FIBRE PRESERVING MAPS
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 Title & Authors
A NIELSEN TYPE NUMBER OF FIBRE PRESERVING MAPS
Lee, Seoung Ho;
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 Abstract
We introduce a Nielsen type number of a fibre preserving map, and show that it is a lower bound for the number of -orbits in the homotopy class. Under suitable conditions we show that it is equal to the Nielsen type relative essential -orbit number. We also give necessary and sufficient conditions for it and the essential -orbit number to coincide.
 Keywords
essential n-orbit classes;Nielsen type numbers;fibre spaces;
 Language
English
 Cited by
 References
1.
R. F. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresman, Glenview, IL, 1971.

2.
P. R. Heath, Product formulae for Nielsen numbers of fibre maps, Pacific J. Math. 117 (1985), no. 2, 267-289. crossref(new window)

3.
P. R. Heath, A Nielsen type number for fibre preserving maps, Topology Appl. 53 (1993), no. 1, 19-35. crossref(new window)

4.
P. R. Heath, R. Piccinini, and C. You, Nielsen-type numbers for periodic points I, in: Topological fixed point theory and applications (Tianjin, 1988), 88-106, Lecture Notes in Math., 1411, Springer, Berlin, 1989.

5.
P. R. Heath, H. Schirmer, and C. You, Nielsen type numbers for periodic points on nonconnected spaces, Topology Appl. 63 (1995), no. 2, 97-116. crossref(new window)

6.
P. R. Heath, H. Schirmer, and C. You, Nielsen type numbers for periodic points on pairs of spaces, Topology Appl. 63 (1995), no. 2, 117-138. crossref(new window)

7.
B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemporary Mathematics 14, American Mathematical Society, Providence, RI 1983.

8.
B. Jiang, S. H. Lee, and M. H. Woo, Reidemeister orbit sets, Fund. Math. 183 (2004), no. 2, 139-156. crossref(new window)

9.
S. H. Lee and Y. S. Yoon, A relative Reidemeister orbit number, Commun. Korean Math. Soc. 21 (2006), no. 1, 193-209. crossref(new window)

10.
H. Schirmer, A relative Nielsen number, Pacific J. Math. 122 (1986), no. 2, 459-473. crossref(new window)

11.
E. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.

12.
C. You, Fixed point classes of a fibre map, Pacific J. Math. 100 (1992), no. 1, 217-241.