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Title

On generalizing the Nielsen coincidence theory to non-oriented manifolds

Authors 1

Affiliations

  1. Department of Mathematics, Agriculture University, Nowoursynowska 166, 02-766 Warszawa, Poland

Abstract

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

Bibliography

  1. [B] R. F. Brown, The Lefschetz Fixed Point Theorem, Glenview, New York, 1971.
  2. [D] R. Dobreńko, The obstruction to the deformation of a map out of a space, Dissertationes Math. (Rozprawy Mat.) 295 (1990).
  3. [DJ] R. Dobreńko and J. Jezierski, The coincidence Nielsen theory on non-orientable manifolds, Rocky Mountain J. Math. 23 (1993), 67-85.
  4. [DK] R. Dobreńko and Z. Kucharski, On the generalization of the Nielsen number, Fund. Math. 134 (1990), 1-14.
  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.
  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.
  10. [Je2] J. Jezierski, The semi-index product formula, Fund. Math. 140 (1992), 99-120.
  11. [Je3] J. Jezierski, The coincidence Nielsen number for maps into real projective spaces, Fund. Math. 140 (1992), 121-136.
  12. [Je4] J. Jezierski, The Nielsen coincidence theory on topological manifolds, Fund. Math. 143 (1993), 167-178.
  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.
  16. [N1] J. Nielsen, Über die Minimalzahl der Fixpunkte bei Abbildungstypen der Ringflächen, Math. Ann. 82 (1929), 83-93.
  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.
Banach Center Publications
1999/49/1
Export to PBN, Opens in new tab
Pages:
189-202
Main language of publication
English
Published
1999
Exact and natural sciences