One-relator groups and proper 3-realizability.
Optics in Croke-Kleiner Spaces
We explore the interior geometry of the CAT(0) spaces , constructed by Croke and Kleiner [Topology 39 (2000)]. In particular, we describe a diffraction effect experienced by the family of geodesic rays that emanate from a basepoint and pass through a certain singular point called a triple point, and we describe the shadow this family casts on the boundary. This diffraction effect is codified in the Transformation Rules stated in Section 3 of this paper. The Transformation Rules have various applications....
Parabolic isometries of CAT(0) spaces and CAT(0) dimensions.
Partial order and collapsibility of 2-complexes
Poincaré duality groups of dimension two.
Poincaré duality groups of dimension two, II.
Products of Conjugacy Classes in a Free Group: a Counterexample.
Question de Whitehead et modules précroisés
Small hyperbolic 3-manifolds with geodesic boundary.
Solvable Groups that are Simply Connected at ... .
Spherical Diagrams and Indentities Among Relations.
Strategies towards a disproof of the general Andrews-Curtis conjecture.
Strong surjectivity of maps from 2-complexes into the 2-sphere
Given a model 2-complex K P of a group presentation P, we associate to it an integer matrix ΔP and we prove that a cellular map f: K P → S 2 is root free (is not strongly surjective) if and only if the diophantine linear system ΔP Y = (f) has an integer solution, here (f)is the so-called vector-degree of f
Subgroups with projective abelianization and trivial multiplicator.
Surface bundles over surfaces of small genus.
Surfaces and the Second Homology of a Group.
Systolic groups acting on complexes with no flats are word-hyperbolic
We prove that if a group acts properly and cocompactly on a systolic complex, in whose 1-skeleton there is no isometrically embedded copy of the 1-skeleton of an equilaterally triangulated Euclidean plane, then the group is word-hyperbolic. This was conjectured by D. T. Wise.
The accessibility of finitely presented groups.
The edge-minimal polyhedral maps of Euler characteristic .
The Homotopoy Type of Four-Dimensional Knot Complements.