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

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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

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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

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  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
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  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. 

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