The Nielsen coincidence theory on topological manifolds

Jerzy Jezierski

Fundamenta Mathematicae (1993)

  • Volume: 143, Issue: 2, page 167-178
  • ISSN: 0016-2736

Abstract

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We generalize the coincidence semi-index introduced in [D-J] to pairs of maps between topological manifolds. This permits extending the Nielsen theory to this class of maps.

How to cite

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Jezierski, Jerzy. "The Nielsen coincidence theory on topological manifolds." Fundamenta Mathematicae 143.2 (1993): 167-178. <http://eudml.org/doc/211999>.

@article{Jezierski1993,
abstract = {We generalize the coincidence semi-index introduced in [D-J] to pairs of maps between topological manifolds. This permits extending the Nielsen theory to this class of maps.},
author = {Jezierski, Jerzy},
journal = {Fundamenta Mathematicae},
keywords = {coincidence semi-index; Nielsen theory},
language = {eng},
number = {2},
pages = {167-178},
title = {The Nielsen coincidence theory on topological manifolds},
url = {http://eudml.org/doc/211999},
volume = {143},
year = {1993},
}

TY - JOUR
AU - Jezierski, Jerzy
TI - The Nielsen coincidence theory on topological manifolds
JO - Fundamenta Mathematicae
PY - 1993
VL - 143
IS - 2
SP - 167
EP - 178
AB - We generalize the coincidence semi-index introduced in [D-J] to pairs of maps between topological manifolds. This permits extending the Nielsen theory to this class of maps.
LA - eng
KW - coincidence semi-index; Nielsen theory
UR - http://eudml.org/doc/211999
ER -

References

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  1. [B] R. Brooks, On removing coincidences of two maps when only one rather than both of them may be deformed by a homotopy, Pacific J. Math. 40 (1972), 45-52. Zbl0235.55006
  2. [D-J] R. Dobreńko and J. Jezierski, The coincidence Nielsen theory on non-orientable manifolds, Rocky Mountain J. Math. 23 (1993), 67-85. Zbl0787.55003
  3. [D-K] R. Dobreńko and Z. Kucharski, On the generalization of the Nielsen number, Fund. Math. 134 (1990), 1-14. Zbl0719.55002
  4. [F] M. Freedman, The topology of four dimensional manifolds, J. Differential Geometry 17 (1982), 357-453. Zbl0528.57011
  5. [Je1] J. Jezierski, The semi-index product formula, Fund. Math. 140 (1992), 99-120. Zbl0811.55003
  6. [Je2] J. Jezierski, The coincidence Nielsen number for maps into real projective spaces, ibid., 121-136. Zbl0811.55002
  7. [Ji1] B. J. Jiang, Fixed point classes from a differential viewpoint, in: Lecture Notes in Math. 886, Springer, 1981, 163-170. 
  8. [Ji2] B. J. Jiang, Lectures on the Nielsen Fixed Point Theory, Contemp. Math. 14, Amer. Math. Soc., Providence 1983. 
  9. [K-S] R. Kirby and L. Siebenmann, Foundational Essays on Topological Manifolds, Smoothings and Triangulations, Ann. of Math. Stud. 88, Princeton University Press, Princeton, 1977. Zbl0361.57004
  10. [Q] F. Quinn, Ends of maps III: Dimensions 4 and 5, J. Differential Geometry 17 (1982), 503-521. Zbl0533.57009
  11. [Sc] M. Scharlemann, Transversality theories in dimension 4, Invent. Math. 33 (1976), 1-14. Zbl0318.57007
  12. [S] H. Schirmer, Mindestzahlen von Koinzidenzpunkten, J. Reine Angew. Math. 194 (1955), 21-39. 
  13. [V] J. Vick, Homology Theory, Academic Press, New York, 1973. 

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