Algebraic linking numbers of knots in 3-manifolds.
Algebraic properties of mapping class groups of surfaces
Algorithmic detection and description of hyperbolic structures on closed 3-manifolds with solvable word problem.
All CAT(0) boundaries of a group of the form H × K are CE equivalent
M. Bestvina has shown that for any given torsion-free CAT(0) group G, all of its boundaries are shape equivalent. He then posed the question of whether they satisfy the stronger condition of being cell-like equivalent. In this article we prove that the answer is "Yes" in the situation where the group in question splits as a direct product with infinite factors. We accomplish this by proving an interesting theorem in shape theory.
All flat manifolds are cusps of hyperbolic orbifolds.
All integral slopes can be Seifert fibered slopes for hyperbolic knots.
All Knot Groups Are Metric.
All knots are algebraic.
All roots of unity are detected by the A-polynomial.
All two dimensions links are null homotopic.
Almost integral TQFTs from simple Lie algebras.
Almost-Bieberbach groups with prime order holonomy
The main issue of this paper is an attempt to find a decomposition theorem for infra-nilmanifolds in the same spirit as a result of A. Vasquez for flat Riemannian manifolds. That is: we look for infra-nilmanifolds with prime order holonomy which can be obtained as a fiber space with a non-trivial nilmanifold as fiber and an infra-nilmanifold as its base. In this perspective, we prove the following algebraic result: if E is an almost-Bieberbach group with prime order holonomy,...
Amenable actions of amalgamated free products of free groups over a cyclic subgroup and generic property
We show that the amalgamated free products of two free groups over a cyclic subgroup admit amenable, faithful and transitive actions on infinite countable sets. This work generalizes the results on such actions for doubles of free group on two generators.
Amenable groups and Euler characteristic.
Amenable Groups and Stabilizers of Measures on the Boundary of a Hadamard Manifold.
Amenable, transitive and faithful actions of groups acting on trees
We study under which condition an amalgamated free product or an HNN-extension over a finite subgroup admits an amenable, transitive and faithful action on an infinite countable set. We show that such an action exists if the initial groups admit an amenable and almost free action with infinite orbits (e.g. virtually free groups or infinite amenable groups). Our result relies on the Baire category Theorem. We extend the result to groups acting on trees.
An Abelian Quotient of the Mapping Class Group ...g.
An Algebraic Classification of some Knots of Codimension Two.
An algorithm of finding planar surfaces in three-manifolds.
An algorithm to detect laminar 3-manifolds.