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ArticleOriginal scientific text

Title

The semi-index product formula

Authors 1

Affiliations

  1. Department of Mathematics, University of Agriculture, Nowoursynowska 166, 02-766 Warszawa, Poland

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| (fb,gb: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(fb,gb).

Bibliography

  1. [DJ] R. Dobreńko and J. Jezierski, The coincidence Nielsen number on non-orientable manifolds, Rocky Mountain J. Math., to appear.
  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.
  4. [J] B. J. Jiang, Lectures on the Nielsen Fixed Point Theory, Contemp. Math. 14, Amer. Math. Soc., Providence, R.I., 1983.
  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.

Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm140/fm14021.pdf

Fundamenta Mathematicae
1991-1992/140/2
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Pages:
99-120
Main language of publication
English
Received
1990-07-23
Accepted
1991-04-08
Published
1992
Exact and natural sciences