ArticleOriginal scientific text
Title
Minimal fixed point sets of relative maps
Authors 1
Affiliations
- Department of Mathematics, Capital Normal University, Beijing 100037, P.R. China
Abstract
Let f: (X,A) → (X,A) be a self map of a pair of compact polyhedra. It is known that f has at least N(f;X,A) fixed points on X. We give a sufficient and necessary condition for a finite set P (|P| = N(f;X,A)) to be the fixed point set of a map in the relative homotopy class of the given map f. As an application, a new lower bound for the number of fixed points of f on Cl(X-A) is given.
Keywords
fixed point class, minimal fixed point set, relative Nielsen number, bipartite graph, matching
Bibliography
- R. F. Brown, The Lefschetz Fixed Point Theorem, Scott and Foresman, Glenview, IL, 1971.
- H P. Hall, On representatives of subsets, J. London Math. Soc. 10 (1935), 26-30.
- B. Jiang, On the least number of fixed points, Amer. J. Math. 102 (1980), 749-763.
- B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemp. Math. 14, Amer. Math. Soc., Providence, RI, 1983.
- H. Schirmer, A relative Nielsen number, Pacific J. Math. 122 (1986), 459-473.
- H. Schirmer, On the location of fixed points on pairs of spaces, Topology Appl. 30 (1988), 253-266.
- W P. Wolfenden, Fixed point sets of deformations of polyhedra with local cut points, Trans. Amer. Math. Soc. 350 (1998), 2457-2471.
- X. Z. Zhao, A relative Nielsen number for the complement, in: Topological Fixed Point Theory and Applications, B. Jiang (ed.), Lecture Notes in Math. 1411, Springer, Berlin, 1989, 189-199.
- X. Z. Zhao, Basic relative Nielsen numbers, in: Topology-Hawaii, World Sci., Singapore, 1992, 215-222.
Pages:
163-180
Main language of publication
English
Received
1998-06-09
Published
1999
Exact and natural sciences