Related papers: The mapping class group of a disk with infinitely …
Homology of braid groups and Artin groups can be related to the study of spaces of curves. We completely calculate the integral homology of the family of smooth curves of genus $g$ with one boundary component, that are double coverings of…
We study those Artin groups which, modulo their centers, are finite index subgroups of the mapping class group of a sphere with at least 5 punctures. In particular, we show that any injective homomorphism between these groups is…
Big mapping class groups are the mapping class groups of infinite-type surfaces, that is, surfaces whose fundamental groups are not finitely generated. While mapping class groups of finite-type surfaces have been extensively studied, the…
We study the automorphism group of graphons (graph limits). We prove that after an appropriate "standardization" of the graphon, the automorphism group is compact. Furthermore, we characterize the orbits of the automorphism group on…
A topology is defined on the mapping class group of a compact connected orientable surface. It is shown that a notion of "genericity" on subsets of the mapping class group arises from this definition. Many plausible results follow from this…
It is proved that the mapping class group of any closed surface with finitely many marked points is quasiisometric to a CAT(0) cube complex. We provide two distinct proofs, one tailored to mapping class groups, and one applying to a larger…
Let $N$ be a closed nonorientable surface with or without marked points. In this paper we prove that, for every finite full subgraph $\Gamma$ of $\mathcal{C}^{\mathrm{two}}(N)$, the right-angled Artin group on $\Gamma$ can be embedded in…
This paper is devoted to the proof of a structural theorem, concerning certain homomorphic images of Artin braid group on $n$ strands in finite symmetric groups. It is shown that any one of these permutation groups is an extension of the…
We study when the mapping class group of an infinite-type surface $S$ admits an action with unbounded orbits on a connected graph whose vertices are simple closed curves on $S$. We introduce a topological invariant for infinite-type…
We develop an analogy between right-angled Artin groups and mapping class groups through the geometry of their actions on the extension graph and the curve graph respectively. The central result in this paper is the fact that each…
We provide evidence both for and against a conjectural analogy between geometrically finite infinite covolume Fuchsian groups and the mapping class group of compact non-orientable surfaces. In the positive direction, we show the complement…
Dehornoy showed that the Artin braid groups $B_n$ are left-orderable. This ordering is discrete, but we show that, for $n >2$ the Dehornoy ordering, when restricted to certain natural subgroups, becomes a dense ordering. Among subgroups…
We study the action of the mapping class group on the real homology of finite covers of a topological surface. We use the homological representation of the mapping class to construct a faithful infinite-dimensional representation of the…
We study $2$-dimensional Artin groups of hyperbolic type from the viewpoint of measure equivalence, and establish rigidity theorems. We first prove that they are boundary amenable. So is every group acting discretely by simplicial…
Hyperelliptic mapping class groups are defined either as the centralizers of hyperelliptic involutions inside mapping class groups of oriented surfaces of finite type or as the inverse images of these centralizers by the natural…
In this monograph, we give an account of the relationship between the algebraic structure of finitely generated and countable groups and the regularity with which they act on manifolds. We concentrate on the case of one--dimensional…
Omori and the author have given an infinite presentation for the mapping class group of a compact non-orientable surface. In this paper, we give more simple infinite presentations for this group.
We show that the twisted conjugacy problem is solvable for large-type Artin groups whose outer automorphism group is finite, generated by graph automorphisms and the global inversion. This includes XXXL Artin groups whose defining graph is…
We investigate the mapping class groups of a class of non-Hausdorff topological spaces which includes finite spaces. We show that the mapping class group of a finite space is isomorphic to the homeomorphism group of its $T_0$ quotient. As a…
This thesis takes Brady's construction of $K(\pi,1)$s for the braid groups as a starting point. It is widely known that this construction can - with the right ingredients - be generalized to Artin groups of finite type. Results of Bessis as…