The Nielsen coincidence theory on topological manifolds

Jerzy Jezierski

Fundamenta Mathematicae (1993)

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

Abstract

top
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

top

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

top
  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. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.