One-relator groups and proper 3-realizability.
Open 3-manifolds and branched coverings: a quick exposition.
Open 3-manifolds, wild subsets of S3 and branched coverings.
In this paper, a representation of closed 3-manifolds as branched coverings of the 3-sphere, proved in [13], and showing a relationship between open 3-manifolds and wild knots and arcs will be illustrated by examples. It will be shown that there exist a 3-fold simple covering p : S3 --> S3 branched over the remarkable simple closed curve of Fox [4] (a wild knot). Moves are defined such that when applied to a branching set, the corresponding covering manifold remains unchanged, while the branching...
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....
OPTi's algorithm for discreteness determination.
Orbites périodiques et courbes pseudo-holomorphes. Application à la conjecture de Weinstein en dimension 3
Orderable 3-manifold groups
We investigate the orderability properties of fundamental groups of 3-dimensional manifolds. Many 3-manifold groups support left-invariant orderings, including all compact -irreducible manifolds with positive first Betti number. For seven of the eight geometries (excluding hyperbolic) we are able to characterize which manifolds’ groups support a left-invariant or bi-invariant ordering. We also show that manifolds modelled on these geometries have virtually bi-orderable groups. The question of virtual orderability...
Ordering Knots
Orientation Reversing Involutions and the First Betti Number for Finite Coverings of 3-Manifolds.
Outer automorphism groups of Bieberbach groups.
Overtwisted open books from sobering arcs.
Ozsváth-Szabó invariants and tight contact three-manifolds; I.