A geometric study of Fibonacci groups.
A group theoretical model for mass-splitting
A lantern lemma.
A note on the rank of self-dual polyhedra
A reconstruction theorem for locally moving groups acting on completely metrizable spaces
Let G be a group which acts by homeomorphisms on a metric space X. We say the action of G is locally moving on X if for every open U ⊆ X there is a g ∈ G such that g↾X ≠ Id while g↾(X∖U) = Id. We prove the following theorem: Theorem A. Let X,Y be completely metrizable spaces and let G be a group which acts on X and Y with locally moving actions. If the orbits of the action of G on X are of the second category in X and the orbits of the action of G on Y are of the second category...
Abelian subgroups of the Torelli group.
Amenability and Ramsey theory
The purpose of this article is to connect the notion of the amenability of a discrete group with a new form of structural Ramsey theory. The Ramsey-theoretic reformulation of amenability constitutes a considerable weakening of the Følner criterion. As a by-product, it will be shown that in any non-amenable group G, there is a subset E of G such that no finitely additive probability measure on G measures all translates of E equally. The analysis of discrete groups will be generalized to the setting...
An elementary approach to the mapping class group of a surface.
An expansion of the Jones representation of genus 2 and the Torelli group.
Cobordism Obstructions to Deforming Isolated Singularities.
Commensurations of the Johnson kernel.
Computer calculation of the degree of maps into the Poincaré homology sphere.
Computing crossed modules induced by an inclusion of a normal subgroup, with applications to homotopy 2-types.
Counting fixed points of a finitely generated subgroup of Aff [C].
Given a finitely generated subgroup G of the group of affine transformations acting on the complex line C, we are interested in the quotient Fix( G)/G. The purpose of this note is to establish when this quotient is finite and in this case its cardinality. We give an application to the qualitative study of polynomial planar vector fields at a neighborhood of a nilpotent singular point.
Dehn twists on nonorientable surfaces
Let be the Dehn twist about a circle a on an orientable surface. It is well known that for each circle b and an integer n, , where I(·,·) is the geometric intersection number. We prove a similar formula for circles on nonorientable surfaces. As a corollary we prove some algebraic properties of twists on nonorientable surfaces. We also prove that if ℳ(N) is the mapping class group of a nonorientable surface N, then up to a finite number of exceptions, the centraliser of the subgroup of ℳ(N) generated...
Des groupes magiques ou quand des sous-groupes libres affines opèrent proprement discontinûment sur
Every Finite Complex has the Homology of a Duality Group.
Explicit resolutions for the binary polyhedral groups and for other central extensions of the triangle gorups.
Finite presentations for the mapping class group via the ordered complex of curves.
Fox pairings and generalized Dehn twists
We introduce a notion of a Fox pairing in a group algebra and use Fox pairings to define automorphisms of the Malcev completions of groups. These automorphisms generalize to the algebraic setting the action of the Dehn twists in the group algebras of the fundamental groups of surfaces. This work is inspired by the Kawazumi–Kuno generalization of the Dehn twists to non-simple closed curves on surfaces.