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In this work, we study the asymptotic geometry of the mapping class group and Teichmuller
space. We introduce tools for analyzing the geometry of “projection” maps from these spaces …

Abstract We study Wilson-'t Hooft loop operators in a class of Script N= 2 superconformal
field theories recently introduced by Gaiotto. In the case that the gauge group is a product of …

We prove that if a normal subgroup of the extended mapping class group of a closed surface
has an element of sufficiently small support, then its automorphism group and abstract …

In all possible cases, we prove that local embeddings between two curve complexes whose
complexities do not increase from domain to codomain are induced by surface …

Let R be a compact, connected, orientable surface of genus g with p boundary components.
The mapping class group ModR ofR is the group of isotopy classes of orientation-preserving …

In this paper, we prove that each injective simplicial map of the arc complex of a compact,
connected, orientable surface with nonempty boundary is induced by a homeomorphism of …

We prove that curve complexes of surfaces are finitely rigid: for every orientable surface S of
finite topological type, we identify a finite subcomplex 𝔛 of the curve complex such that every …

In this article we interpret the relations defining the Grothendieck-Teichmüller group GT as
cocycle relations for certain non-commutative co-homology sets, which we compute using a …

We study the ideal triangulation graph T (S) of an oriented punctured surface S of finite type.
We show that if S is not the sphere with at most three punctures or the torus with one …