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ArticleOriginal scientific text

Title

A note on the converse of the Lefschetz theorem for G-maps

Authors 1, 2

Affiliations

  1. Technical University of Gdańsk, Department of Applied Mathematics, 80-952 Gdańsk, Poland
  2. Universidad de La Laguna, Facultad de Matemáticas, La Laguna, Tenerife, Spain

Abstract

The purpose of this note is to prove the converse of the Lefschetz fixed point theorem (CLT) together with an equivariant version of the converse of the Lefschetz deformation theorem (CDT) in the category of finite G-simplicial complexes, where G is a finite group.

Keywords

ENG
equivariant Nielsen number, G-simplicial complex, equivariant map, fixed point

Bibliography

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  3. [B] R. Brown, The Lefschetz Fixed Point Theorem, Scott and Foresman, 1971.
  4. [E-S] S. Eilenberg and N. Steenrod, Foundations of Algebraic Topology, Princeton Univ. Press, 1952.
  5. [F-Wo] E. Fadell and P. Wong, On deforming G-maps to be fixed point free, Pacific J. Math. 132 (1988), 277-281.
  6. [V] A. Vidal, On equivariant deformation of maps, Publ. Mat. 32 (1988), 115-121.
  7. [W] D. Wilczyński, Fixed point free equivariant homotopy classes, Fund. Math. 123 (1984), 47-60.
  8. [Wo] P. Wong, Equivariant Nielsen fixed point theory for G-maps, Pacific J. Math. 150 (1991), 179-200.
Annales Polonici Mathematici
1993/58/2
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Pages:
177-183
Main language of publication
English
Received
1992-08-28
Published
1993
Exact and natural sciences