# Fifteen problems about the mapping class groups

@article{Ivanov2006FifteenPA, title={Fifteen problems about the mapping class groups}, author={Nikolai V. Ivanov}, journal={arXiv: Geometric Topology}, year={2006} }

This paper presents fifteen problems about mapping class groups. It is an expanded and updated version of the author's preprint "Ten problems on the mapping class groups". The paper will appear in the book "Problems on Mapping Class Groups and Related Topics", ed. by B. Farb, Proc. Symp. Pure Math. series, Amer. Math. Soc.

## 29 Citations

### Problems, questions, and conjectures about mapping class groups

- MathematicsProceedings of Symposia in Pure Mathematics
- 2019

We discuss a number of open problems about mapping class groups of surfaces. In particular, we discuss problems related to linearity, congruence subgroups, cohomology, pseudo-Anosov stretch factors,…

### Big Flip Graphs and Their Automorphism Groups

- Mathematics
- 2022

In this paper, we study the relationship between the mapping class group of an infinite-type surface and the simultaneous flip graph, a variant of the flip graph for infinite-type surfaces defined by…

### Rotating families, and the structure of some normal subgroups in groups acting on hyperbolic spaces

- Mathematics
- 2010

This question is “Problem 2.12(A)” in Kirby’s list, and is often attributed to Penner, Long, and McCarthy in the early ’80s. It is also recorded by Ivanov [17, Problems 3], and Farb refers to it in…

### A tale of two groups: arithmetic groups and mapping class groups

- Mathematics
- 2011

In this chapter, we discuss similarities, differences and interaction between two natural and important classes of groups: arithmetic subgroups Γ of Lie groups G and mapping class groups Modg,n of…

### Normal generators for mapping class groups are abundant

- MathematicsCommentarii Mathematici Helvetici
- 2022

We provide a simple criterion for an element of the mapping class group of a closed surface to have normal closure equal to the whole mapping class group. We apply this to show that every nontrivial…

### Abelian quotients of subgroups of the mapping class group and higher Prym representations

- MathematicsJ. Lond. Math. Soc.
- 2013

If this conjecture holds for some genus, then it also holds for all larger genera, and a family of linear representations of the mapping class group that are called the higher Prym representations generalize the classical symplectic representation.

### The congruence subgroup problem for pure braid groups: Thurston's proof

- Mathematics
- 2010

In this article we present an unpublished proof of W. Thurston that pure braid groups have the congruence subgroup property.

### On power subgroups of mapping class groups

- Mathematics
- 2009

In the first part of this paper we prove that the mapping class subgroups generated by the $D$-th powers of Dehn twists (with $D\geq 2$) along a sparse collection of simple closed curves on an…

### The congruence subgroup problem for braid groups: Thurston's proof

- Mathematics
- 2009

In this article we present an unpublished proof of W. Thursto n that pure braid groups have the congruence subgroup property.

### Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces

- Mathematics
- 2011

We introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generalization of the peripheral structure of a…

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