# Lefschetz coincidence formula on non-orientable manifolds

Daciberg Gonçalves; Jerzy Jezierski

Fundamenta Mathematicae (1997)

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

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

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