Related papers: Property (FA) and lattices in SU(2,1)
We study the automorphism group Aut(G) of a free product G of finite cyclic groups. We investigate the question in which cases Aut(G) has Serre's property FA. In the case of two or three free factors, we prove that Aut(G) does not have…
We give a new proof of the fact that finite bipartite graphs cannot be axiomatized by finitely many first-order sentences among FINITE graphs. (This fact is a consequence of a general theorem proved by L. Ham and M. Jackson, and the…
We find the smallest possible covolume for lattices in PGL3(Q2), show that there are exactly two lattices with this covolume, and describe them explicitly. They are commensurable, and one of them appeared in Mumford's construction of his…
In this paper we study structural properties of residuated lattices that are idempotent as monoids. We provide descriptions of the totally ordered members of this class and obtain counting theorems for the number of finite algebras in…
We introduce the blockwise gluing construction. This describes residuated integral chains which can be decomposed into (possibly) partial algebras, stacked one on top of the other, and such that elements in a certain component multiply in…
Let $L=diag(1,1,\ldots,1,-1)$ and $M=diag(1,1,\ldots,1,-2)$ be the lattices of signature $(n,1)$. We consider the groups $\Gamma=SU(L,\mathcal{O}_K)$ and $\Gamma'=SU(M,\mathcal{O}_K)$ for an imaginary quadratic field…
The article establishes a long list of rigidity properties of lattices in G = SO(n,1) with n>=3 and G = SU(n,1) with n>=2 that are analogous to superrigidity of lattices in higher-rank Lie groups. The arguments are set in the context of…
In this paper we use techniques from convex projective geometry to produce many new examples of thin subgroups of lattices in special linear groups that are isomorphic to the fundamental groups of finite volume hyperbolic manifolds. More…
Property FW is a natural combinatorial weakening of Kazhdan's Property T. We prove that the group of piecewise homographic self-transformations of the real projective line, has "few" infinite subgroups with Property FW. In particular, no…
The paper is devoted to a study of certain fixed point properties, and their relatives, in the context of full automorphism groups of countable rooted trees. Namely, we study Serre's property (FA'), also called unsplittability, property…
$N$-Metaplectic categories, unitary modular categories with the same fusion rules as $SO(N)_2$, are prototypical examples of weakly integral modular categories. As such, a conjecture of the second author would imply that images of the braid…
We find bases for naturally defined lattices over certain rings of integers in the SU(2)-TQFT-theory modules of surfaces. We consider the TQFT where the Kauffman's A variable is a root of unity of order four times an odd prime. As an…
We show that the group factors of ICC lattices in either SO(n,1) or SU(n,1), n \geq 2, are strongly solid in the sense of Ozawa and Popa. This strengthens a result of Ozawa and Popa showing that these factors do not have Cartan subalgebras.
We identify a class of symmetric algebras over a complete discrete valuation ring $\mathcal O$ of characteristic zero to which the characterisation of Kn\"orr lattices in terms of stable endomorphism rings in the case of finite group…
In the present article, we provide examples of fake quadrics, that is, minimal complex surfaces of general type with the same numerical invariants as the smooth quadric in $\PP ^3$ which are quotients of the bidisc by an irreducible lattice…
We produce an example of an irreducible discrete subgroup in the product $SL(2,\R)\times SL(2,\R)$ which is not a lattice. This answers a question asked in [15].
We extend and attempt to clarify recent results which showed possible problems for universality for the gauge group SU(2). We suggest that the presence of artifacts actually distorts the mixed-coupling plane. This implies that a separation…
We characterize well-founded algebraic lattices by means of forbidden subsemilattices of the join-semilattice made of their compact elements. More specifically, we show that an algebraic lattice $L$ is well-founded if and only if $K(L)$,…
We start a systematic analysis of the first-order model theory of free lattices. Firstly, we prove that the free lattices of finite rank are not positively indistinguishable, as there is a positive $\exists \forall$-sentence true in…
We prove that, under mild assumptions, a lattice in a product of semi-simple Lie group and a totally disconnected locally compact group is, in a certain sense, arithmetic. We do not assume the lattice to be finitely generated or the ambient…