Towards Nielsen-Thurston classification for surfaces of infinite type: well-tempered homeomorphisms

Mladen Bestvina; Federica Fanoni; Jing Tao

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arXiv · 2303.12413

Towards Nielsen-Thurston classification for surfaces of infinite type: well-tempered homeomorphisms

Mladen Bestvina·Federica Fanoni·Jing Tao

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Abstract

We introduce and study tempered mapping classes of surfaces of infinite type. These are maps for which curves under iteration do not accumulate onto geodesic laminations with non-proper leaves, but only on unions of possibly intersecting curves or proper lines. Assuming an additional finiteness condition on the accumulation set, we prove a Nielsen-Thurston-type classification theorem. We prove that for such maps there is a canonical decomposition of the surface into invariant subsurfaces on which the first return is either periodic or a translation.

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BibTeX RIS

Mladen Bestvina, Federica Fanoni, Jing Tao. 2023-03-22. Towards Nielsen-Thurston classification for surfaces of infinite type: well-tempered homeomorphisms. https://arxiv.org/abs/2303.12413

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