Related papers: Diffeomorphisms groups of tame Cantor sets and Tho…
Suppose M is a non-compact connected n-manifold without boundary, DD(M) is the group of C^\infty-diffeomorphisms of M endowed with the Whitney C^\infty-topology and DD_0(M) is the identity connected component of DD(M), which is an open…
In this paper we introduce toric rings of multicomplexes. We show how to compute the divisor class group and the class of the canonical module when the toric ring is normal. In the special case that the multicomplex is a discrete…
Computational Group Theory is applied to indexed objects (tensors, spinors, and so on) with dummy indices. There are two groups to consider: one describes the intrinsic symmetries of the object and the other describes the interchange of…
Following an idea of Gon\c{c}alvez, Guaschi and Ocampo on the usual braid group we construct crystallographic and Bieberbach groups as (sub)quotients of the generalized braid group associated to an arbitrary complex reflection group.
In this manuscript we prove that if two cuspidal plane curves have equivalent braid monodromy factorizations, then they are smoothly isotopic in the plane. As a consequence of this and the Chisini conjecture, we obtain that if two…
The purpose of this note is twofold. In the first part we observe that two finitely generated non-amenable groups are quasi-isometric if and only if they admit topologically orbit equivalent Cantor minimal actions. In particular, free…
We give examples of minimal diffeomorphisms of compact connected manifolds which are not topologically orbit equivalent, but whose transformation group C*-algebras are isomorphic. The examples show that the following properties of a minimal…
We show that R. Thompson's group $T$ is a maximal subgroup of the group $V$. The argument provides examples of foundational calculations which arise when expressing elements of $V$ as products of transpositions of basic clopen sets in…
Complex braid groups are the natural generalizations of braid groups associated to arbitrary (finite) complex reflection groups. We investigate several methods for computing the homology of these groups. In particular, we get the Poincar\'e…
The isomorphism number (resp. isogeny cutoff) of a p-divisible group D over an algebraically closed field is the least positive integer m such that D[p^m] determines D up to isomorphism (resp. up to isogeny). We show that these invariants…
New constructions in group homology allow us to manufacture high-dimensional manifolds with controlled simplicial volume. We prove that for every dimension bigger than 3 the set of simplicial volumes of orientable closed connected manifolds…
We make available some results about model theory cyclically ordered groups. We start with a classification of complete theories of divisible abelian cyclically ordered groups. Then we look at the cyclically ordered groups where the only…
A topological group G is profinite if it is compact and totally disconnected. Equivalently, G is the inverse limit of a surjective system of finite groups carrying the discrete topology. We discuss how to represent a countably based…
We introduce some new symmetric tensor categories based on the combinatorics of trees: a discrete family $\mathcal{D}(n)$, for $n \ge 3$ an integer, and a continuous family $\mathcal{C}(t)$, for $t \ne 1$ a complex number. The construction…
Virtually every known pair of isospectral but nonisometric manifolds - with as most famous members isospectral bounded $\mathbb{R}$-planar domains which makes one "not hear the shape of a drum" [13] - arise from the (group theoretical)…
We provide the first examples of finitely generated simple groups that are amenable (and infinite). This follows from a general existence result on invariant states for piecewise-translations of the integers. The states are obtained by…
We study a family of Thompson-like groups built as rearrangement groups of fractals from [BF19], each acting on a Wa\.zewski dendrite. Each of these is a finitely generated group that is dense in the full group of homeomorphisms of the…
If Gamma is any finite graph, then the unlabelled configuration space of n points on Gamma, denoted UC^n(Gamma), is the space of n-element subsets of Gamma. The braid group of Gamma on n strands is the fundamental group of UC^n(Gamma). We…
Let $\theta$ be a nondegenerate skew symmetric real $d$ by $d$ matrix, and let $A_{\theta}$ be the corresponding simple higher dimensional noncommutative torus. Suppose that $d$ is odd, or that $d$ is greater or equal to 4 and the entries…
Discrete subgroups of SL(2,R) are well understood, and classified by the geometry of the corresponding hyperbolic surfaces. Discrete subgroups of higher-rank semisimple Lie groups, such as SL(n,R) for n>2, remain more mysterious. While…