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Tame maps of surfaces of infinite type

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OGG - Operators, Graphs, Groups

A cornerstone of low-dimensional topology is the Nielsen–Thurston classification theorem, which provides a blueprint for understanding homeomorphisms of finite-type surfaces up to homotopy. However, extending this theory to surfaces of infinite type remains an elusive goal. A key difficulty is the behavior of curves under iteration, which can exhibit pathologies that do not arise in the finite-type setting. To address these challenges, we introduce the notion of tame maps, a class of homeomorphisms with non-mixing dynamics. In this talk, I will present some recent progress on extending the classification theory to such maps. This is joint work with Mladen Bestvina and Federica Fanoni.

This talk is part of the Isaac Newton Institute Seminar Series series.

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