Lefschetz coincidence formula on non-orientable manifolds

Daciberg Gonçalves; Jerzy Jezierski

Fundamenta Mathematicae (1997)

  • Volume: 153, Issue: 1, page 1-23
  • ISSN: 0016-2736

Abstract

top
We generalize the Lefschetz coincidence theorem to non-oriented manifolds. We use (co-) homology groups with local coefficients. This generalization requires the assumption that one of the considered maps is orientation true.

How to cite

top

Gonçalves, Daciberg, and Jezierski, Jerzy. "Lefschetz coincidence formula on non-orientable manifolds." Fundamenta Mathematicae 153.1 (1997): 1-23. <http://eudml.org/doc/212212>.

@article{Gonçalves1997,
abstract = {We generalize the Lefschetz coincidence theorem to non-oriented manifolds. We use (co-) homology groups with local coefficients. This generalization requires the assumption that one of the considered maps is orientation true.},
author = {Gonçalves, Daciberg, Jezierski, Jerzy},
journal = {Fundamenta Mathematicae},
keywords = {manifold; coincidence; orientation true maps; twisted coefficients; Lefschetz number; Nielsen class},
language = {eng},
number = {1},
pages = {1-23},
title = {Lefschetz coincidence formula on non-orientable manifolds},
url = {http://eudml.org/doc/212212},
volume = {153},
year = {1997},
}

TY - JOUR
AU - Gonçalves, Daciberg
AU - Jezierski, Jerzy
TI - Lefschetz coincidence formula on non-orientable manifolds
JO - Fundamenta Mathematicae
PY - 1997
VL - 153
IS - 1
SP - 1
EP - 23
AB - We generalize the Lefschetz coincidence theorem to non-oriented manifolds. We use (co-) homology groups with local coefficients. This generalization requires the assumption that one of the considered maps is orientation true.
LA - eng
KW - manifold; coincidence; orientation true maps; twisted coefficients; Lefschetz number; Nielsen class
UR - http://eudml.org/doc/212212
ER -

References

top
  1. [Bd] G. Bredon, Geometry and Topology, Grad. Texts in Math. 139, Springer, New York, 1993. 
  2. [B] R. F. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresman and Co., New York, 1971. Zbl0216.19601
  3. [BS] R. F. Brown and H. Schirmer, Nielsen coincidence theory and coincidence producing maps for manifolds with boundary, Topology Appl. 46 (1992), 65-79. Zbl0757.55002
  4. [DJ] R. Dobreńko and J. Jezierski, The coincidence Nielsen theory on non-orientable manifolds, Rocky Mountain J. Math. 23 (1993), 67-85. Zbl0787.55003
  5. [FH] E. Fadell and S. Husseini, Fixed point theory for non-simply connected manifolds, Topology 30 (1981), 53-92. Zbl0453.55002
  6. [G1] D. L. Gonçalves, Indices for coincidence classes and the Lefschetz formula for non-orientable manifolds, preprint, Mathematisches Institut, Universität Heidelberg. 
  7. [G2] D. L. Gonçalves, Coincidence theory for maps from a complex into a manifold, preprint. 
  8. [GO] D. L. Gonçalves and E. Oliveira, The Lefschetz coincidence numbers for maps on compact surfaces, preprint, Department of Mathematics, UFSCAR, S ao Carlos. 
  9. [Je] J. Jezierski, The Nielsen coincidence theory on topological manifolds, Fund. Math. 143 (1993), 167-178. Zbl0789.55002
  10. [Ji] B. Jiang, Lectures on the Nielsen Fixed Point Theory, Contemp. Math. 14, Amer. Math. Soc., Providence, 1983. 
  11. [M] K. Mukherjea, Coincidence theory for manifolds with boundary, Topology Appl. 46 (1992), 23-39. Zbl0757.55003
  12. [O] P. Olum, Obstructions to extensions and homotopies, Ann. of Math. 52 (1950), 1-50. Zbl0038.36601
  13. [Sp1] E. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966. 
  14. [Sp2] E. Spanier, Duality in topological manifolds, in: Colloque de Topologie Tenu à Bruxelles, Centre Belge de Recherches Mathématiques, 1966, 91-111. 
  15. [V] J. Vick, Homology Theory, Academic Press, New York, 1973. 
  16. [W1] C. T. C. Wall, Surgery of non-simply-connected manifolds, Ann. of Math. 84 (1966), 217-276. Zbl0149.20602
  17. [W2] C. T. C. Wall, On Poincaré complex I, Ann. of Math. 86 (1967), 213-245. 
  18. [Wh] G. W. Whitehead, Elements of Homotopy Theory, Springer, New York, 1978. 

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.