On generalizing the Nielsen coincidence theory to non-oriented manifolds

Jerzy Jezierski

Banach Center Publications (1999)

  • Volume: 49, Issue: 1, page 189-202
  • ISSN: 0137-6934

Abstract

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We give an outline of the Nielsen coincidence theory emphasizing differences between the oriented and non-oriented cases.

How to cite

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Jezierski, Jerzy. "On generalizing the Nielsen coincidence theory to non-oriented manifolds." Banach Center Publications 49.1 (1999): 189-202. <http://eudml.org/doc/208958>.

@article{Jezierski1999,
abstract = {We give an outline of the Nielsen coincidence theory emphasizing differences between the oriented and non-oriented cases.},
author = {Jezierski, Jerzy},
journal = {Banach Center Publications},
keywords = {Nielsen theory; coincidence point; defective classes},
language = {eng},
number = {1},
pages = {189-202},
title = {On generalizing the Nielsen coincidence theory to non-oriented manifolds},
url = {http://eudml.org/doc/208958},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Jezierski, Jerzy
TI - On generalizing the Nielsen coincidence theory to non-oriented manifolds
JO - Banach Center Publications
PY - 1999
VL - 49
IS - 1
SP - 189
EP - 202
AB - We give an outline of the Nielsen coincidence theory emphasizing differences between the oriented and non-oriented cases.
LA - eng
KW - Nielsen theory; coincidence point; defective classes
UR - http://eudml.org/doc/208958
ER -

References

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  1. [B] R. F. Brown, The Lefschetz Fixed Point Theorem, Glenview, New York, 1971. Zbl0216.19601
  2. [D] R. Dobreńko, The obstruction to the deformation of a map out of a space, Dissertationes Math. (Rozprawy Mat.) 295 (1990). Zbl0728.55002
  3. [DJ] R. Dobreńko and J. Jezierski, The coincidence Nielsen theory on non-orientable manifolds, Rocky Mountain J. Math. 23 (1993), 67-85. Zbl0787.55003
  4. [DK] R. Dobreńko and Z. Kucharski, On the generalization of the Nielsen number, Fund. Math. 134 (1990), 1-14. Zbl0719.55002
  5. [Dl] A. Dold, Lectures on Algebraic Topology, Springer, New York, 1972. 
  6. [G] D. L. Gonçalves, Indices for coincidence classes and the Lefschetz formula for non-oriented manifolds, preprint, Math. Institut, Univ. Heidelberg. 
  7. [GJ] D. L. Gonçalves and J. Jezierski, Lefschetz coincidence formula on non-orientable manifolds, Fund. Math. 153 (1997), 1-23. Zbl0884.55001
  8. [H] M. Hirsch, Differential Topology, Springer, New York, 1976. 
  9. [Je1] J. Jezierski, The Nielsen number product formula for coincidences, Fund. Math. 134 (1989), 183-212. Zbl0715.55002
  10. [Je2] J. Jezierski, The semi-index product formula, Fund. Math. 140 (1992), 99-120. Zbl0811.55003
  11. [Je3] J. Jezierski, The coincidence Nielsen number for maps into real projective spaces, Fund. Math. 140 (1992), 121-136. Zbl0811.55002
  12. [Je4] J. Jezierski, The Nielsen coincidence theory on topological manifolds, Fund. Math. 143 (1993), 167-178. Zbl0789.55002
  13. [Ji1] B. J. Jiang, Lectures on the Nielsen Fixed Point Theory, Contemp. Math. 14, Amer. Math. Soc., Providence, 1983. 
  14. [Ji2] B. J. Jiang, Fixed point classes from a differential viewpoint, in: Lecture Notes in Math. 886, Springer, 1981, 163-170. 
  15. [L] S. Lefschetz, Intersections and transformations of complexes and manifolds, TAMS 28 (1926) 1-49. Zbl52.0572.02
  16. [N1] J. Nielsen, Über die Minimalzahl der Fixpunkte bei Abbildungstypen der Ringflächen, Math. Ann. 82 (1929), 83-93. Zbl47.0527.03
  17. [N2] J. Nielsen, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen, I, II, III, Acta Math. 50 (1927), 189-358; 53 (1929), 1-76; 58 (1932), 87-167. 
  18. [Sch] H. Schirmer, Mindestzahlen von Koinzidenzpunkten, J. Reine Angew. Math. 194 (1955), 21-39. 
  19. [Sp1] E. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966. 
  20. [Sp2] E. Spanier, Duality in topological manifolds, in: Colloque de Topologie Tenu à Bruxelles (Centre de Recherche Mathématiques), 1966, 91-111. 
  21. [V] J. Vick, Homology Theory, Academic Press, New York, 1973. 
  22. [Y] C. Y. You, Fixed points of a fibre map, Pacific J. Math. 100 (1982), 217-241. 

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