# Minimal fixed point sets of relative maps

Fundamenta Mathematicae (1999)

- Volume: 162, Issue: 2, page 163-180
- ISSN: 0016-2736

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topZhao, Xue. "Minimal fixed point sets of relative maps." Fundamenta Mathematicae 162.2 (1999): 163-180. <http://eudml.org/doc/212417>.

@article{Zhao1999,

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.},

author = {Zhao, Xue},

journal = {Fundamenta Mathematicae},

keywords = {fixed point class; minimal fixed point set; relative Nielsen number; bipartite graph; matching; minimal number; by-passing; Nielsen relation},

language = {eng},

number = {2},

pages = {163-180},

title = {Minimal fixed point sets of relative maps},

url = {http://eudml.org/doc/212417},

volume = {162},

year = {1999},

}

TY - JOUR

AU - Zhao, Xue

TI - Minimal fixed point sets of relative maps

JO - Fundamenta Mathematicae

PY - 1999

VL - 162

IS - 2

SP - 163

EP - 180

AB - 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.

LA - eng

KW - fixed point class; minimal fixed point set; relative Nielsen number; bipartite graph; matching; minimal number; by-passing; Nielsen relation

UR - http://eudml.org/doc/212417

ER -

## References

top- [1] R. F. Brown, The Lefschetz Fixed Point Theorem, Scott and Foresman, Glenview, IL, 1971. Zbl0216.19601
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- [3] B. Jiang, On the least number of fixed points, Amer. J. Math. 102 (1980), 749-763. Zbl0455.55001
- [4] B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemp. Math. 14, Amer. Math. Soc., Providence, RI, 1983.
- [5] H. Schirmer, A relative Nielsen number, Pacific J. Math. 122 (1986), 459-473. Zbl0553.55001
- [6] H. Schirmer, On the location of fixed points on pairs of spaces, Topology Appl. 30 (1988), 253-266. Zbl0664.55003
- [7] W P. Wolfenden, Fixed point sets of deformations of polyhedra with local cut points, Trans. Amer. Math. Soc. 350 (1998), 2457-2471. Zbl0897.54015
- [8] 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.
- [9] X. Z. Zhao, Basic relative Nielsen numbers, in: Topology-Hawaii, World Sci., Singapore, 1992, 215-222. Zbl1039.55503

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