The averaged Dehn function relative to a given probability measure.
The Bass conjecture and growth in groups
We discuss Bass's conjecture on the vanishing of the Hattori-Stallings rank from the viewpoint of geometric group theory. It is noted that groups without u-elements satisfy this conjecture. This leads in particular to a simple proof of the conjecture in the case of groups of subexponential growth.
The braid groups of the projective plane.
The Burau representation is not faithful for .
The cd-index of Bruhat intervals.
The central heights of stability groups of series in vector spaces
We compute the central heights of the full stability groups of ascending series and of descending series of subspaces in vector spaces over fields and division rings. The aim is to develop at least partial right analogues of results on left Engel elements and related nilpotent radicals in such proved recently by Casolo & Puglisi, by Traustason and by the current author. Perhaps surprisingly, while there is an absolute bound on these central heights for descending series, for ascending series...
The chameleon groups of Richards J. Thompson: automorphisms and dynamics
The classification of groups in which every product of four elements can be reordered
The cohomology algebras of orientable Seifert manifolds and applications to Lusternik-Schnirelmann category
This note gives a complete description of the cohomology algebra of any orientable Seifert manifold with ℤ/p coefficients, for an arbitrary prime p. As an application, the existence of a degree one map from an orientable Seifert manifold onto a lens space is completely determined. A second application shows that the Lusternik-Schnirelmann category for a large class of Seifert manifolds is equal to 3, which in turn is used to verify the Ganea conjecture for these Seifert manifolds.
The combinatorial derivation and its inverse mapping
Let G be a group and P G be the Boolean algebra of all subsets of G. A mapping Δ: P G → P G defined by Δ(A) = {g ∈ G: gA ∩ A is infinite} is called the combinatorial derivation. The mapping Δ can be considered as an analogue of the topological derivation d: P X→ P X, A ↦ A d, where X is a topological space and A d is the set of all limit points of A. We study the behaviour of subsets of G under action of Δ and its inverse mapping ∇. For example, we show that if G is infinite and I is an ideal in...
The Conjugacy Problem for Free Products of Sixth-Groups with Cyclic Amalgamation.
The conjugacy problem for groups, and Higman embeddings.
The conjugacy problem for relatively hyperbolic groups.
The conjugacy-vectors of all relative holomorphs of an elementary Abelian group of order 16
The Conway-Norton algebras for ?(6,3), ?(7,3), F'24, and their full automorphism groups.
The co-rank conjecture for 3-manifold groups.
The Coxeter group .
The Decomposition numbers of the Hecke algebra of type F4.
The Dehn functions of and
For at least 3, the Dehn functions of and are exponential. Hatcher and Vogtmann proved that they are at most exponential, and the complementary lower bound in the case was established by Bridson and Vogtmann. Handel and Mosher completed the proof by reducing the lower bound for bigger than 3 to the case . In this note we give a shorter, more direct proof of this last reduction.
The Derived Series of a Join of Subnormal Sugroups.