The relative coincidence Nielsen number

Jerzy Jezierski

Fundamenta Mathematicae (1996)

  • Volume: 149, Issue: 1, page 1-18
  • ISSN: 0016-2736

Abstract

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We define a relative coincidence Nielsen number N r e l ( f , g ) for pairs of maps between manifolds, prove a Wecken type theorem for this invariant and give some formulae expressing N r e l ( f , g ) by the ordinary Nielsen numbers.

How to cite

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Jezierski, Jerzy. "The relative coincidence Nielsen number." Fundamenta Mathematicae 149.1 (1996): 1-18. <http://eudml.org/doc/212106>.

@article{Jezierski1996,
abstract = {We define a relative coincidence Nielsen number $N_\{rel\}(f,g)$ for pairs of maps between manifolds, prove a Wecken type theorem for this invariant and give some formulae expressing $N_\{rel\}(f,g)$ by the ordinary Nielsen numbers.},
author = {Jezierski, Jerzy},
journal = {Fundamenta Mathematicae},
keywords = {coincidence; Nielsen numbers; manifolds},
language = {eng},
number = {1},
pages = {1-18},
title = {The relative coincidence Nielsen number},
url = {http://eudml.org/doc/212106},
volume = {149},
year = {1996},
}

TY - JOUR
AU - Jezierski, Jerzy
TI - The relative coincidence Nielsen number
JO - Fundamenta Mathematicae
PY - 1996
VL - 149
IS - 1
SP - 1
EP - 18
AB - We define a relative coincidence Nielsen number $N_{rel}(f,g)$ for pairs of maps between manifolds, prove a Wecken type theorem for this invariant and give some formulae expressing $N_{rel}(f,g)$ by the ordinary Nielsen numbers.
LA - eng
KW - coincidence; Nielsen numbers; manifolds
UR - http://eudml.org/doc/212106
ER -

References

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  1. [B] R. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresman and Co., New York, 1971. Zbl0216.19601
  2. [BS] R. Brown and H. Schirmer, Nielsen coincidence theory and coincidence-producing maps for manifolds with boundary, Topology Appl. 46 (1992), 65-79. Zbl0757.55002
  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. [Je1] J. Jezierski, The Nielsen number product formula for coincidences, Fund. Math. 134 (1989), 183-212. Zbl0715.55002
  5. [Je2] J. Jezierski, The semi-index product formula, ibid. 140 (1992), 99-120. 
  6. [Je3] J. Jezierski, The coincidence Nielsen number for maps into real projective spaces, ibid. 140 (1992), 121-136. Zbl0811.55002
  7. [Je4] J. Jezierski, The coincidence Nielsen theory on topological manifolds, ibid. 143 (1993), 167-178. 
  8. [Je5] J. Jezierski, The Lefschetz coincidence number on non-orientable manifolds, submitted. 
  9. [Ji] B. J. Jiang, Lectures on the Nielsen Fixed Point Theory, Contemp. Math. 14, Amer. Math. Soc., Providence, 1983. 
  10. [S1] H. Schirmer, Mindestzahlen von Koinzidenzpunkten, J. Reine Angew. Math. 194 (1955), 21-39. 
  11. [S2] H. Schirmer, A relative Nielsen number, Pacific J. Math. 122 (1986), 459-473. Zbl0553.55001
  12. [Y] C. Y. You, Fixed points of a fibre map, ibid. 100 (1982), 217-241. 

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