Related papers: Embeddings into Thompson's group $V$ and $co\mathc…

We prove that the word problem of the Brin-Thompson group nV over a finite generating set is coNP-complete for every n \ge 2. It is known that the groups nV are an infinite family of infinite, finitely presented, simple groups. We also…

A VB-groupoid is a Lie groupoid equipped with a compatible linear structure. In this paper, we describe a correspondence, up to isomorphism, between VB-groupoids and 2-term representations up to homotopy of Lie groupoids. Under this…

Let G be a finite group acting on a finite dimensional real vector space V. We denote by P(V) the projective space associated to V. In this paper we compute in a very explicit way the rank of the equivariant complex K-theory of V and P(V),…

Leighton's Graph Covering Theorem states that if two finite graphs have the same universal covering tree, then they also have a common finite degree cover. Bass and Kulkarni gave an alternative proof of this fact using tree lattices. We…

Thompson's group $V$ has a rich variety of subgroups, containing all finite groups, all finitely generated free groups and all finitely generated abelian groups, the finitary permutation group of a countable set, as well as many wreath…

We introduce and develop a categorification of the theory of Real representations of finite groups. In particular, we generalize the categorical character theory of Ganter--Kapranov and Bartlett to the Real setting. Given a Real…

If $G$ is a finite group or a torus, it is known that there is an isomorphism between the Grothendieck group of homotopy representations and that of generalized homotopy representations for $G$. We prove that there is such an isomorphism…

The relative Novikov conjecture states that the relative higher signatures of manifolds with boundary are invariant under orientation-preserving homotopy equivalences of pairs. In this paper, we study the relative Baum-Connes assembly map…

In the first part of this note, we introduce Tietze transformations for $L$-presentations. These transformations enable us to generalize Tietze's theorem for finitely presented groups to invariantly finitely $L$-presented groups. Moreover,…

In the quest in constructing conformal field theories (CFT) Jones has discovered a beautiful and deep connection between CFT, Richard Thompson's groups and knot theory. This led to a powerful functorial framework for constructing actions of…

We determine exactly which graph products, also known as Right Angled Artin Groups, embed into Richard Thompson's group $V$. It was shown by Bleak and Salazar-Diaz that $\mathbb{Z}^2 * \mathbb{Z}$ was an obstruction. We show that this is…

The Kashiwara-Vergne (KV) conjecture is a property of the Campbell-Hausdorff series put forward in 1978. It has been settled in the positive by E. Meinrenken and the first author in 2006. In this paper, we study the uniqueness issue for the…

We provide a new tableau model from which one can easily deduce the characters of finite-dimensional irreducible polynomial representations of the special orthogonal group $SO_n(\mathbb{C})$. This model originates from the representation…

We study Deaconu-Renault groupoids corresponding to surjective local homeomorphisms on locally compact, Hausdorff, second countable, totally disconnected spaces, and we characterise when the C*-algebras of these groupoids are AF embeddable.…

We show that the comma category $(\mathcal{F}\downarrow\mathbf{Grp})$ of groups under the free group functor $\mathcal{F}: \mathbf{Set} \to \mathbf{Grp}$ contains the category $\mathbf{Gph}$ of simple graphs as a full coreflective…

For various series of complex semi-simple Lie algebras $\fg (t)$ equipped with irreducible representations $V(t)$, we decompose the tensor powers of $V(t)$ into irreducible factors in a uniform manner, using a tool we call {\it diagram…

We provide new examples of $\mathrm{C}^*$-selfless groups and inclusions. In particular, we prove that the commensurator group ${\rm Comm}(H)$ of a torsion-free hyperbolic group $H$ is $\mathrm{C}^*$-selfless. Our approach involves showing…

The $n$-dimensional affine Weyl-Heisenberg group is a Lie group typically parameterized as $G_{aWH} = \mathbb{T} \times \mathbb{R}^n \times \widehat{\mathbb{R}^n} \times \mathrm{GL}(n, \mathbb{R})$, generated by all translation, dilation,…

We introduce the Hermitian-invariant group $\Gamma_f$ of a proper rational map $f$ between the unit ball in complex Euclidean space and a generalized ball in a space of typically higher dimension. We use properties of the groups to define…

We show that diagram groups can be viewed as fundamental groups of spaces of positive paths on directed 2-complexes (these spaces of paths turn out to be classifying spaces). Thus diagram groups are analogs of second homotopy groups,…