Jing Tao

Tame maps of surfaces of infinite type

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.