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

Annales Polonici Mathematici (1993)

- Volume: 58, Issue: 2, page 177-183
- ISSN: 0066-2216

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topM. Izydorek, and A. Vidal. "A note on the converse of the Lefschetz theorem for G-maps." Annales Polonici Mathematici 58.2 (1993): 177-183. <http://eudml.org/doc/262435>.

@article{M1993,

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.},

author = {M. Izydorek, A. Vidal},

journal = {Annales Polonici Mathematici},

keywords = {equivariant Nielsen number; G-simplicial complex; equivariant map; fixed point; converse of the Lefschetz fixed point theorem; equivariant; Lefschetz deformation theorem; finite group},

language = {eng},

number = {2},

pages = {177-183},

title = {A note on the converse of the Lefschetz theorem for G-maps},

url = {http://eudml.org/doc/262435},

volume = {58},

year = {1993},

}

TY - JOUR

AU - M. Izydorek

AU - A. Vidal

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

JO - Annales Polonici Mathematici

PY - 1993

VL - 58

IS - 2

SP - 177

EP - 183

AB - 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.

LA - eng

KW - equivariant Nielsen number; G-simplicial complex; equivariant map; fixed point; converse of the Lefschetz fixed point theorem; equivariant; Lefschetz deformation theorem; finite group

UR - http://eudml.org/doc/262435

ER -

## References

top- [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. Zbl0523.57027
- [B] R. Brown, The Lefschetz Fixed Point Theorem, Scott and Foresman, 1971. Zbl0216.19601
- [E-S] S. Eilenberg and N. Steenrod, Foundations of Algebraic Topology, Princeton Univ. Press, 1952. Zbl0047.41402
- [F-Wo] E. Fadell and P. Wong, On deforming G-maps to be fixed point free, Pacific J. Math. 132 (1988), 277-281. Zbl0612.58007
- [V] A. Vidal, On equivariant deformation of maps, Publ. Mat. 32 (1988), 115-121. Zbl0649.57003
- [W] D. Wilczyński, Fixed point free equivariant homotopy classes, Fund. Math. 123 (1984), 47-60. Zbl0548.55002
- [Wo] P. Wong, Equivariant Nielsen fixed point theory for G-maps, Pacific J. Math. 150 (1991), 179-200. Zbl0691.55004

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