Fee Local Semigroup Constructions.
Fields of tangent sets and Hofmann cones.
Filters and semigroup properties.
Fine convergence in free groups
Finite dimensional continuous representations of compact regular semigroups.
Finite point compactifications of (N, +).
Foliations, groupoids and Baum-Connes conjecture.
Foliations induced by congruences.
Foliations, locally Lie groupoids and holonomy
Free actions of free groups on countable structures and property (T)
We show that if G is a non-archimedean, Roelcke precompact Polish group, then G has Kazhdan's property (T). Moreover, if G has a smallest open subgroup of finite index, then G has a finite Kazhdan set. Examples of such G include automorphism groups of countable ω-categorical structures, that is, the closed, oligomorphic permutation groups on a countable set. The proof uses work of the second author on the unitary representations of such groups, together with a separation result for infinite permutation...
Free groups and semigroups in ßN.
Free groups in ßN which miss the minimal ideal.
Free groups of semigroups in semi-simple Lie groups.
Free non-archimedean topological groups
We study free topological groups defined over uniform spaces in some subclasses of the class of non-archimedean groups. Our descriptions of the corresponding topologies show that for metrizable uniformities the corresponding free balanced, free abelian and free Boolean groups are also metrizable. Graev type ultra-metrics determine the corresponding free topologies. Such results are in a striking contrast with free balanced and free abelian topological groups cases (in standard varieties). Another...
Free products of topological groups with equal uniformities, I
Free products of topological groups with equal uniformities, II
Free topological inverse semigroups.
From a topological theory of semigroup to a geometric one.
From double Lie groups to quantum groups
It is shown, using geometric methods, that there is a C*-algebraic quantum group related to any double Lie group (also known as a matched pair of Lie groups or a bicrossproduct Lie group). An algebra underlying this quantum group is the algebra of a differential groupoid naturally associated with the double Lie group.
Function spaces and fixed point properties: a Galois connection.