Classification of mapping classes of infinite-type surfaces
Mapping classes of surfaces of finite type have been classified by Nielsen and Thurston. For surfaces of infinite type (e.g. surfaces of infinite genus), no such classification is known. I will talk about the difficulties that arise when trying to generalize the Nielsen-Thurston classification to infinite-type surfaces and present a first result in this direction, concerning maps which - loosely speaking - do not show any pseudo-Anosov behavior. Joint work with Mladen Bestvina and Jing Tao.
