This article is concerned with conjugacy problems arising in homeomorphisms group, Hom(F ), of non-compact subsets F of normed vector spaces E. Given two homeomorphisms f and g in Hom(F ), it is shown how the existence of a conjugacy may be related to the existence of a common generalized eigenfunction of the associated Koopman operators. This common eigenfunction serves to build a topology on ...

In this paper we prove some mainly asymptotic results concerning the irreducible character degrees of .nite groups of Lie type. Applications are given to the study of the mixing time of random walks on these groups, with certain conjugacy classes as generating sets. In various situations we show that the mixing time is 2; this seems to be the .rst determination of an exact bounded mixing time f...

Let G be a group and φ an automorphism of G. Two elements x,y are said to φ-twisted conjugate if y=gxφ(g)−1 for some g∈G. A has the R∞-property number conjugacy classes is infinite every In this paper, we prove that big mapping class MCG(S) possesses under suitable conditions on infinite-type surface S. As application, also only it satisfies S∞-property.

We show how, by making use of a new basis of the IIB supergravity axion-dilaton coset, SL(2,R)/SO(2), 7-branes that belong to different conjugacy classes of the duality group SL(2,R) naturally couple to IIB supergravity with appropriate source terms characterized by an SL(2,R) charge matrix Q. The conjugacy classes are determined by the value of the determinant of Q. The (p, q) 7-branes are the...

In this paper, we analyze the Borel complexity of the topological conjugacy relation on Toeplitz subshifts. More specifically, we prove that topological conjugacy of Toeplitz subshifts with separated holes is hyperfinite. Indeed, we show that the topological conjugacy relation is hyperfinite on a larger class of Toeplitz subshifts which we call Toeplitz subshifts with growing blocks. This resul...

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...

Each graph and choice of a commutative ring gives rise to an associated graphical group. In this article, we introduce investigate polynomials that enumerate conjugacy classes groups over finite fields according their sizes.