Related papers: The braided Ptolemy-Thompson group $T^*$ is asynch…

We define pseudo-Garside groups and prove a theorem about them parallel to Garside's result on the word problem for the usual braid groups. The main novelty is that the set of simple elements can be infinite. We introduce a group B=B(Z^n)…

The second author showed how Katsura's construction of the C*-algebra of a topological graph E may be twisted by a Hermitian line bundle L over the edge space E. The correspondence defining the algebra is obtained as the completion of the…

In the present paper, we show that many combinatorial and topological objects, such as maps, hypermaps, three-dimensional pavings, constellations and branched coverings of the two--sphere admit any given finite automorphism group. This…

In this article, we introduce a new family of groups, called Chambord groups and constructed from braided strand diagrams associated to specific semigroup presentations. It includes the asymptotically rigid mapping class groups previously…

In this note, we show that the sets of all stable commutator lengths in the braided Ptolemy-Thompson groups are equal to non-negative rational numbers.

We show that many normal subgroups of the braid group modulo its centre, and of the mapping class group of a sphere with marked points, have the property that their automorphism and abstract commensurator groups are mapping class groups of…

The main result of this article is that any braided (resp. annular, planar) diagram group $D$ splits as a short exact sequence $1 \to R \to D \to S \to 1$ where $R$ is a subgroup of some right-angled Artin group and $S$ a subgroup of…

We introduce the notion of measurable bounded cohomology for measured groupoids, extending continuous bounded cohomology of locally compact groups. We show that the measurable bounded cohomology of the semidirect groupoid associated to a…

This note serves as a short and reader-friendly introduction to twisted Brin-Thompson groups, which were recently constructed by Belk and the author to provide a family of simple groups with a variety of interesting properties. Most…

In this paper, we introduce a symmetric continuous cohomology of topological groups. This is obtained by topologizing a recent construction due to Staic (J. Algebra 322 (2009), 1360-1378), where a symmetric cohomology of abstract groups is…

We show that the automorphism groups of countably categorical linear orders are extremely amenable. Using methods of Kechris, Pestov, and Todorcevic, we use this fact to derive a structural Ramsey theorem for certain families of finite…

We show that Thompson's group F is the symmetry group of the "generic idempotent". That is, take the monoidal category freely generated by an object A and an isomorphism A \otimes A --> A; then F is the group of automorphisms of A.

In a recent paper Uffe Haagerup and Kristian Knudsen Olesen show that for Richard Thompson's group $T$, if there exists a finite set $H$ which can be decomposed as disjoint union of sets $H_1$ and $H_2$ with $\sum_{g\in…

The braid groups B_n can be defined as the mapping class group of the n-punctured disc. The Lawrence-Krammer representation of the braid group B_n is the induced action on a certain twisted second homology of the space of unordered pairs of…

Given a measurable twisted action of a second-countable, locally compact group G on a separable C*-algebra A, we prove the existence of a topology on AxG making it a continuous bundle, whose cross sectional C*-algebra is isomorphic to the…

We construct a braided version of Thompson's group V.

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…

A left orderable completely metrizable topological group is exhibited containing Artin's braid group on infinitely many strands. The group is the mapping class group (rel boundary) of the closed unit disk with a sequence of interior…

This paper demonstrates the uniformly finite homology developed by Block and Weinberger and its relationship to amenable spaces via applications to the Cayley graph of Thompson's Group F. In particular, a certain class of subgraph of F is…

The paper is devoted to prove a version of Milnor-Moore Theorem for connected braided bialgebras that are infinitesimally cocommutative. Namely in characteristic different from 2, we prove that, for a given connected braided bialgebra $A$…