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

M. Izydorek; A. Vidal

Annales Polonici Mathematici (1993)

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

Abstract

top
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.

How to cite

top

M. 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
  1. [B-G] L. Borsari and D. Gonçalves, G-deformations to fixed point free maps via obstruction theory, preprint. 
  2. [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
  3. [B] R. Brown, The Lefschetz Fixed Point Theorem, Scott and Foresman, 1971. Zbl0216.19601
  4. [E-S] S. Eilenberg and N. Steenrod, Foundations of Algebraic Topology, Princeton Univ. Press, 1952. Zbl0047.41402
  5. [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
  6. [V] A. Vidal, On equivariant deformation of maps, Publ. Mat. 32 (1988), 115-121. Zbl0649.57003
  7. [W] D. Wilczyński, Fixed point free equivariant homotopy classes, Fund. Math. 123 (1984), 47-60. Zbl0548.55002
  8. [Wo] P. Wong, Equivariant Nielsen fixed point theory for G-maps, Pacific J. Math. 150 (1991), 179-200. Zbl0691.55004

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.