# The semi-index product formula

Fundamenta Mathematicae (1992)

• Volume: 140, Issue: 2, page 99-120
• ISSN: 0016-2736

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## Abstract

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We consider fibre bundle maps (...) where all spaces involved are smooth closed manifolds (with no orientability assumption). We find a necessary and sufficient condition for the formula    |ind|(f,g:A) = |ind| (f̅,g̅: p(A)) |ind| $\left({f}_{b},{g}_{b}:{p}^{-1}\left(b\right)\cap A\right)$ to hold, where A stands for a Nielsen class of (f,g), b ∈ p(A) and |ind| denotes the coincidence semi-index from [DJ]. This formula enables us to derive a relation between the Nielsen numbers N(f,g), N(f̅,g̅) and $N\left({f}_{b},{g}_{b}\right)$.

## How to cite

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Jezierski, Jerzy. "The semi-index product formula." Fundamenta Mathematicae 140.2 (1992): 99-120. <http://eudml.org/doc/211940>.

@article{Jezierski1992,
abstract = {We consider fibre bundle maps (...) where all spaces involved are smooth closed manifolds (with no orientability assumption). We find a necessary and sufficient condition for the formula    |ind|(f,g:A) = |ind| (f̅,g̅: p(A)) |ind| $(f_b,g_b:p^\{-1\}(b) ∩ A)$ to hold, where A stands for a Nielsen class of (f,g), b ∈ p(A) and |ind| denotes the coincidence semi-index from [DJ]. This formula enables us to derive a relation between the Nielsen numbers N(f,g), N(f̅,g̅) and $N(f_b,g_b)$.},
author = {Jezierski, Jerzy},
journal = {Fundamenta Mathematicae},
keywords = {Nielsen class; coincidence semi-index; Nielsen numbers},
language = {eng},
number = {2},
pages = {99-120},
title = {The semi-index product formula},
url = {http://eudml.org/doc/211940},
volume = {140},
year = {1992},
}

TY - JOUR
AU - Jezierski, Jerzy
TI - The semi-index product formula
JO - Fundamenta Mathematicae
PY - 1992
VL - 140
IS - 2
SP - 99
EP - 120
AB - We consider fibre bundle maps (...) where all spaces involved are smooth closed manifolds (with no orientability assumption). We find a necessary and sufficient condition for the formula    |ind|(f,g:A) = |ind| (f̅,g̅: p(A)) |ind| $(f_b,g_b:p^{-1}(b) ∩ A)$ to hold, where A stands for a Nielsen class of (f,g), b ∈ p(A) and |ind| denotes the coincidence semi-index from [DJ]. This formula enables us to derive a relation between the Nielsen numbers N(f,g), N(f̅,g̅) and $N(f_b,g_b)$.
LA - eng
KW - Nielsen class; coincidence semi-index; Nielsen numbers
UR - http://eudml.org/doc/211940
ER -

## References

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1. [DJ] R. Dobreńko and J. Jezierski, The coincidence Nielsen number on non-orientable manifolds, Rocky Mountain J. Math., to appear. Zbl0787.55003
2. [H] M. Hirsch, Differential Topology, Springer, New York 1976.
3. [Je] J. Jezierski, The Nielsen number product formula for coincidences, Fund. Math. 134 (1989), 183-212. Zbl0715.55002
4. [J] B. J. Jiang, Lectures on the Nielsen Fixed Point Theory, Contemp. Math. 14, Amer. Math. Soc., Providence, R.I., 1983. Zbl0512.55003
5. [V] J. Vick, Homology Theory, Academic Press, New York 1976.
6. [W] J. A. Wolf, Spaces of Constant Curvature, Univ. of California, Berkeley 1972.
7. [Y] C. Y. You, Fixed points of a fibre map, Pacific J. Math. 100 (1982), 217-241.

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