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...

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.

The principal character of a representation the free group rank two into PSL(2, C) is triple complex numbers that determines an irreducible uniquely up to conjugacy. It central problem in geometry discrete groups and low dimensional topology determine when such represents not virtually abelian, Kleinian group. A classical necessary condition J{\o}rgensen's inequality. Here we use certainly shif...

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.

Inspired by a series of papers initiated in 2015 Berth\'e et al., we introduce new condition called suffix-connectedness. We show that the groups generated return sets uniformly recurrent suffix-connected language lie single conjugacy class subgroups free group. Moreover, rank this only depends on number connected components extension graph empty word. also how to explicitly compute representat...