# The semi-index product formula

Fundamenta Mathematicae (1992)

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

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topJezierski, 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

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

## Citations in EuDML Documents

top- Jerzy Jezierski, The coincidence Nielsen number for maps into real projective spaces
- Jerzy Jezierski, The relative coincidence Nielsen number
- Jerzy Jezierski, The Nielsen coincidence theory on topological manifolds
- Jerzy Jezierski, On generalizing the Nielsen coincidence theory to non-oriented manifolds

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