The semi-index product formula

• Autorzy: Jerzy Jezierski
• Języki publikacji: EN

Abstrakty

EN

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 $N(f_b,g_b)$.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1991-1992
• Tom: 140
• Numer: 2
• Strony: 99-120

Daty

wydano

1992

otrzymano

1990-07-23

poprawiono

1991-04-08

poprawiono

1991-07-24

Twórcy

autor

Jerzy Jezierski

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

Bibliografia

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