We show that the group 3i{M) of pseudoisotopy classes of diffeomorphisms of a manifold of dimension > 5 and of finite fundamental group is commensurable to an arithmetic group. As a result n0{DiffM) is a group of finite type. Let M be an «-dimensional closed smooth manifold, where n > 5, and let DiffM be the group of diffeomorphisms of M. The space DiffM (it is a topological space with the C°°-...

Introduction Gromov's Polynomial Growth Theorem [Gro81] characterizes the class of virtually nilpotent groups by their asymptotic geometry. Since Gromov's theorem it has been a major open question (see, e.g. [GH91]) to find an appropriate generalization for solvable groups. This paper gives the first step in that direction. One fundamental class of examples of finitely-generated solvable groups...

Culler's theorem states that for a finitely generated free group F, of rank at least 2, any finite subgroup of Out(F) fixes a point in Outer Space. This theorem is comparable to Nieslen Realization: for a closed surface with negative Euler characteristic, any finite subgroup of the mapping class group fixes a point in the Teichmüller sapce for the surface as proved by Kerckhoff. For nonnegative...

A finite simple graph Γ determines a right-angled Artin group GΓ, with one generator for each vertex v, and with one commutator relation vw = wv for each pair of vertices joined by an edge. The Bestvina-Brady group NΓ is the kernel of the projection GΓ → Z, which sends each generator v to 1. We establish precisely which graphs Γ give rise to quasi-Kähler (respectively, Kähler) groups NΓ. This y...

A finite simple graph Γ determines a right-angled Artin group GΓ, with one generator for each vertex v, and with one commutator relation vw = wv for each pair of vertices joined by an edge. The Bestvina-Brady group NΓ is the kernel of the projection GΓ → Z, which sends each generator v to 1. We establish precisely which graphs Γ give rise to quasi-Kähler (respectively, Kähler) groups NΓ. This y...

(Here ΛE is a suitable period lattice commensurable with the Néron lattice of E.) The function Φ, which is transcendental as a function of τ , enjoys the following notable algebraicity property, a consequence of the theory of complex multiplication: Theorem HP: Let K ⊂ C be a quadratic imaginary extension of Q, and let K denote its maximal abelian extension. If τ belongs to H ∩ K, then Φ(τ) bel...

This paper presents a flexible querying system of fuzzy RDF annotations which consists in translating fuzzy RDF annotations into fuzzy conceptual graphs and using an “approximate”-projection operation in order to compare fuzzy query graphs with fuzzy annotation graphs. The fuzzy sets in the query graphs having a semantic of preferences are compared with the fuzzy sets in the annotation graphs h...