Related papers: Operad groups and their finiteness properties

We show a homological result for the class of planar or symmetric operad groups: We show that under certain conditions, group (co)homology of such groups with certain coefficients vanishes in all dimensions, provided it vanishes in…

If $\phi$ is an automorphism of a group $G$ and $x,y\in G$, we say that $x$ and $y$ are $\phi$-twisted conjugates if there exists an $z\in G$ such that $y=z.x.\phi(z^{-1})$. This is an equivalence relation. If there are infinitely many…

We give an explicit description of the rigidification of an $\infty$-operad as a simplicial operad. This description is based on the notion of dendroidal necklace, extending work of Dugger and Spivak from the categorical context to the…

We develop a rigidity criterion to show that in simplicial model categories with a compatible symmetric monoidal structure, operad structures can be automatically lifted along certain maps. This is applied to obtain an unpublished result of…

In 1984 Brown and Geoghegan proved that Thompson's group $F$ is of type $\textrm{F}_\infty$, making it the first example of an infinite dimensional torsion-free group of type $\textrm{F}_\infty$. Over the decades a different, shorter proof…

We show that labelled Thompson groups and twisted Brin--Thompson groups are all acyclic. This allows us to prove several new embedding results for groups. First, every group of type $F_n$ embeds quasi-isometrically as a subgroup of an…

We construct a finitely presented group with property (T) which can not act on on reasonable spaces. Such group is constructed using an generalization of Hall embedding theorem, where property (T) is added at the expense of weakening the…

The word problem for Thompson's group $F$ has a solution, but it remains unknown whether $F$ is automatic or has a finite or regular convergent (terminating and confluent) rewriting system. We show that the group $F$ admits a natural…

We introduce the notion of uniform exactness, or uniform amenability at infinity, for discrete groups and prove it for a wide class of groups containing free groups and their limit groups. This shows a novel strong convergence phenomenon…

This paper gives an explicit description of the categorical operad whose algebras are precisely symmetric monoidal categories. This allows us to place the operad in a sequence of four, and therefore a sequence of four successively stricter…

The space of unordered configurations of distinct points in the plane is aspherical, with Artin's braid group as its fundamental group. Remarkably enough, the space of ordered configurations of distinct points on the real projective line,…

We define a category $\mathsf{List}$ whose objects are sets and morphisms are mappings which assign to an element in the domain an ordered sequence (list) of elements in the codomain. We introduce and study a category of simplicial objects…

We study the bounded cohomology of certain groups acting on the Cantor set. More specifically, we consider the full group of homeomorphisms of the Cantor set as well as Thompson's group $V$. We prove that both of these groups are boundedly…

As applications of Kadison's Pythageorean and carpenter's theorems, the Schur-Horn theorem, and Thompson's theorem, we obtain an extension of Thompsons theorem to compact operators and use these ideas to give a characterization of diagonals…

We introduce a symmetric operad $\square p$ ("box-op") which describes a certain calculus of rectangular labeled ``boxes''. Algebras over $\square p$, which we call box operads, have appeared under the name of fc multicategories in work by…

We describe a Grothendieck construction for non-symmetric operads with values in categories, and hence in groupoids and posets. The construction produces a 2-category which is operadically fibered over the category D of finite non-empty…

The structure of a $k$-fold monoidal category as introduced by Balteanu, Fiedorowicz, Schw\"anzl and Vogt can be seen as a weaker structure than a symmetric or even braided monoidal category. In this paper we show that it is still…

By extending type theory with a universe of definitionally associative and unital polynomial monads, we show how to arrive at a definition of opetopic type which is able to encode a number of fully coherent algebraic structures. In…

Let F be the (Thompson's) group < x_0, x_1 | [x_0x_1^-1, x_0^-ix_1 x_0^i], i=1,2 >. We study the structure of F-limit groups. Let G_n= < y_1,..., y_m, x_0,x_1 | [x_0x_1^-1,x_0^-1x_1x_0],[x_0x_1^-1,x_0^-2x_1x_0^2], y_j^-1g_j,n(x_0,x_1),…

We introduce a finiteness property for braided fusion categories, describe a conjecture that would characterize categories possessing this, and verify the conjecture in a number of important cases. In particular we say a category has F if…