## 1. Classifying big mapping classes

In the finite-type setting, the Nielsen–Thurston classification says that every mapping class is either periodic or reducible (or both), or else it is pseudo-Anosov. Can we give a classification of big mapping classes?-
#### Problem 1.1.

[Priyam Patel] Does every big mapping class either preserve a metric or preserve a lamination? -
#### Problem 1.2.

Is there a dynamical description of all mapping classes that do not preserve any (possibly infinite) multicurve? -
This was proposed as an "easier version" of Problem 1.2.
#### Problem 1.3.

[Kasra Rafi] Let $f$ be an (irreducible) big mapping class and $\alpha$ a simple closed curve. Does the sequence $f^n(\alpha)$ converge to a lamination? -
#### Problem 1.4.

[Autumn Kent] Is there a natural bordification of Teichmüller space for big surfaces? -
#### Problem 1.5.

[Priyam Patel] How should handle shifts fit into a classification scheme for mapping classes? -
In the finite-type setting, a mapping class has a representative that’s a hyperbolic isometry for some hyperbolic metric exactly when it is periodic.
#### Problem 1.7.

[org.aimpl.user:jlanier8@gatech.edu] Characterize the big mapping classes that can be realized by hyperbolic isometries. -
#### Problem 1.8.

[Katie Mann] Give a classification of big mapping classes by understanding their dynamics on some combinatorial complex associated with the surface. -
#### Problem 1.9.

[Nic Brody] Characterize big mapping classes whose mapping tori are hyperbolic.

Cite this as: *AimPL: Surfaces of infinite type, available at http://aimpl.org/genusinfinity.
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