Topological Quantum Field Theories are closely related to representations of Mapping Class Groups of surfaces. Considering the case of the TQFTs derived from the Kauffman bracket, we describe the central extension coming from this representation, which is just a projective extension.
The objective of this paper is to give two descriptions of the -free products of archimedean -groups and to establish some properties for the -free products. Specifically, it is proved that -free products satisfy the weak subalgebra property.
We compare the special rank of the factors of the upper central series and terms of the lower central series of a group. As a consequence we are able to show some generalizations of a theorem of Reinhold Baer.
We use subgroup distortion to determine the rate of escape of a simple random walk on a class of polycyclic groups, and we show that the rate of escape is invariant under changes of generating set for these groups. For metabelian groups, we define a stronger form of subgroup distortion which applies to non-finitely generated subgroups. Under this hypothesis, we compute the rate of escape for certain random walks on some abelian-by-cyclic groups via a comparison to the toppling of a dissipative abelian...
Let G be a group generated by r elements . Among the reduced words in of length n some, say , represent the identity element of the group G. It has been shown in a combinatorial way that the 2nth root of has a limit, called the cogrowth exponent with respect to the generators . We show by analytic methods that the numbers vary regularly, i.e. the ratio is also convergent. Moreover, we derive new precise information on the domain of holomorphy of γ(z), the generating function associated...
We consider actions of automorphism groups of free groups by semisimple isometries on complete CAT(0) spaces. If n ≥ 4 then each of the Nielsen generators of Aut(Fₙ) has a fixed point. If n = 3 then either each of the Nielsen generators has a fixed point, or else they are hyperbolic and each Nielsen-generated ℤ⁴ ⊂ Aut(F₃) leaves invariant an isometrically embedded copy of Euclidean 3-space 𝔼³ ↪ X on which it acts as a discrete group of translations with the rhombic dodecahedron as a Dirichlet...
The profinite topology on any abstract group , is one such that the fundamental system of neighborhoods of the identity is given by all its subgroups of finite index. We say that a group has the Ribes-Zalesskii property of rank , or is RZ with a natural number, if any product of finitely generated subgroups is closed in the profinite topology on . And a group is said to have the Ribes-Zalesskii property or is RZ if it is RZ for any natural number . In this paper we characterize groups...