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

Alexander Fel'shtyn

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arXiv · math/9910129

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

Alexander Fel'shtyn

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Abstract

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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Alexander Fel'shtyn. 2000-01-13. Nielsen zeta function, 3-manifolds and asymptotic expansions in Nielsen theory. https://arxiv.org/abs/math/9910129

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