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

• Autorzy: M. Izydorek , A. Vidal
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

equivariant Nielsen number   G-simplicial complex   equivariant map   fixed point  

Kategorie tematyczne

• 55M20: Fixed points and coincidences
• 57S17: Finite transformation groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1993
• Tom: 58
• Numer: 2
• Strony: 177-183

Daty

wydano

1993

otrzymano

1992-08-28

Twórcy

autor

M. Izydorek

• Technical University of Gdańsk, Department of Applied Mathematics, 80-952 Gdańsk, Poland

autor

A. Vidal

• Universidad de La Laguna, Facultad de Matemáticas, La Laguna, Tenerife, Spain

Bibliografia

• [B-G] L. Borsari and D. Gonçalves, G-deformations to fixed point free maps via obstruction theory, preprint.
• [Bo] C. Bowszyc, On the components of the principal part of a manifold with a finite group action, Fund. Math. 115 (1983), 229-233.
• [B] R. Brown, The Lefschetz Fixed Point Theorem, Scott and Foresman, 1971.
• [E-S] S. Eilenberg and N. Steenrod, Foundations of Algebraic Topology, Princeton Univ. Press, 1952.
• [F-Wo] E. Fadell and P. Wong, On deforming G-maps to be fixed point free, Pacific J. Math. 132 (1988), 277-281.
• [V] A. Vidal, On equivariant deformation of maps, Publ. Mat. 32 (1988), 115-121.
• [W] D. Wilczyński, Fixed point free equivariant homotopy classes, Fund. Math. 123 (1984), 47-60.
• [Wo] P. Wong, Equivariant Nielsen fixed point theory for G-maps, Pacific J. Math. 150 (1991), 179-200.