Nielsen zeta function, 3-manifolds and asymptotic expansions in Nielsen theory

Details Nielsen zeta function, 3-manifolds and asymptotic expansions in Nielsen theory Nielsen zeta function, 3-manifolds and asymptotic expansions in Nielsen theory

1999-10-24

arxiv.org/abs/math/9910129v2

Mathematics

Dynamical Systems

15 pages, Latex, section 2 revised

Scientific paper

We prove that the Nielsen zeta function is a rational function or a radical of a rational function for orientation preserving homeomorphisms on closed orientable 3-dimensional manifolds which are special Haken or Seifert manifolds. In the case of pseudo-Anosov homeomorphism of surface we compute an asymptotic for the number of twisted conjugacy classes or for the number of Nielsen fixed point classes whose norm is at most $x$.

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