Some problems on mapping class groups and moduli space

By Benson Farb. 2006

125 citations recorded by the source corpus.

This paper presents a number of problems about mapping class groups and moduli space. 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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6abf003ea6fdbbb5ab92aa30fcaffcc03f9109a4

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

THE DIMENSION OF THE TORELLI GROUP (2007, background): “For g ≥ 2 and any k, Farb gives the lower bound g−1 for cd(Nk(Sg)) by constructing a free abelian subgroup of Nk(Sg) of rank g − 1 [14].”
Right-angled Artin groups and a generalized isomorphism problem for finitely generated subgroups of mapping class groups (2010, background): “It is an open problem to solve the isomorphism problem for finitely presented subgroups of Modg,p (see Farb’s article [21]).”
Semisimple actions of mapping class groups on CAT(0) spaces (2009, background): “[Farb 2006℄ B. Farb, Some problems on mapping lass groups and moduli spa e, in "Problemson mapping lass groups and related topi s" (B. Farb, ed.)”
Statistically convex-cocompact actions of groups with contracting elements (2016, background): “n−l)+!l+logc+logn n ≤!0: Hence, the set of non-contractingf elements NCis growth tight: the proposition 7.2 is proved. The proof of Theorem 7.1 is nished. 7.4. Growth rate of contracting elements. In [34], B. Farb originally conjectured that the set of pseudo-Anosov elements is generic with respect ”