We study topological properties of conjugacy classes in Polish groups, with emphasis on automorphism groups of homogeneous countable structures. We first consider the existence of dense conjugacy classes (the topological Rokhlin property). We then characterize when an automorphism group admits a comeager conjugacy class (answering a question of Truss) and apply this to show that the homeomorphi...

The theoretical framework of General Recognition Theory (GRT; Ashby & Townsend, Psychological Review, 93, 154-179, 1986) coupled with the empirical analysis tools of Multidimensional Signal Detection Analysis (MSDA; Kadlec & Townsend, Multidimensional models of perception and recognition, pp. 181-228, 1992) have become one important method for assessing dimensional interactions in perceptual de...

We prove that the fundamental group of any Seifert 3-manifold is conjugacy separable. That is, conjugates may be distinguished in finite quotients or, equivalently, conjugacy classes are closed in the pro-finite topology.

in this work we consider conjugacy of elements and parabolic subgroups‎ ‎in details‎, ‎in a new class of artin groups‎, ‎introduced in an earlier work‎, ‎which may contain arbitrary parabolic subgroups‎. ‎in particular‎, ‎we find‎ ‎algorithmically minimal representatives of elements in a conjugacy class‎ ‎and also an algorithm to pass from one minimal representative to the others‎.

We discuss time complexity of The Conjugacy Problem in HNN-extensions of groups, in particular, in Miller’s groups. We show that for “almost all”, in some explicit sense, elements, the Conjugacy Problem is decidable in cubic time. It is worth noting that the Conjugacy Problem in a Miller group may have be undecidable. Our results show that “hard” instances of the problem comprise a negligibly s...

Abstract We characterize conjugacy classes of isometries odd prime order in unimodular ${\mathbb {Z}}$-lattices. This is applied to give a complete classification non-symplectic automorphisms the known deformation types irreducible holomorphic symplectic manifolds up and birational conjugacy.

We discuss residual finiteness and several related separability conditions for the class of monoid acts, namely weak subact separability, strong complete separability. For each these four conditions, we investigate which monoids have property that all their (finitely generated) acts satisfy condition. In particular, prove that: over a finite are completely separable (and hence other three condi...

In aggregation theory, the admissibility condition for clustering together components to be aggregated is blockwise weak separability, which also is the condition needed to separate out sectors of the economy. Although weak separability is thereby of central importance in aggregation and index number theory and in econometrics, prior attempts to produce statistical tests of weak separability ha...

When data schemata are enriched with expressive constraints that aim at representing the domain of interest, in order to answer queries one needs to consider the logical theory consisting of both the data and the constraints. Query answering in such a context is called ontological query answering. Commonly adopted database constraints in this field are tuple-generating dependencies (TGDs) and e...