On the classification of compact surfaces admitting cellular decompositions. (Sur la classification des surfaces compactes qui admettent décomposition cellulaire.)
On the classification of tight contact structures. I.
On the cohomology of the classifying space of the gauge group over some 4-complexes
On the colored Jones polynomials of ribbon links, boundary links and Brunnian links
Habiro gave principal ideals of in which certain linear combinations of the colored Jones polynomials of algebraically-split links take values. The author proved that the same linear combinations for ribbon links, boundary links and Brunnian links are contained in smaller ideals of generated by several elements. In this paper, we prove that these ideals also are principal, each generated by a product of cyclotomic polynomials.
On the complexity of braids
We define a measure of “complexity” of a braid which is natural with respect to both an algebraic and a geometric point of view. Algebraically, we modify the standard notion of the length of a braid by introducing generators , which are Garside-like half-twists involving strings through , and by counting powered generators as instead of simply . The geometrical complexity is some natural measure of the amount of distortion of the times punctured disk caused by a homeomorphism. Our main...
On the complexity of graph-manifolds.
On the Conjugacy Problem for Knot Groups.
On the connectivity of skeletons of pseudomanifolds with boundary
In this note we show that -skeletons and -skeletons of -pseudomanifolds with full boundary are -connected graphs and -connected -complexes, respectively. This generalizes previous results due to Barnette and Woon.
On the covering space and the automorphism group of the covering space.
On the cut number of a 3-manifold.
On the cut point conjecture.
On the discrete Godbillon-Vey invariant and Dehn surgery on geodesic flows
On the dynamics and the fixed subgroup of a free group automorphism.
On the dynamics of (left) orderable groups
We develop dynamical methods for studying left-orderable groups as well as the spaces of orderings associated to them. We give new and elementary proofs of theorems by Linnell (if a left-orderable group has infinitely many orderings, then it has uncountably many) and McCleary (the space of orderings of the free group is a Cantor set). We show that this last result also holds for countable torsion-free nilpotent groups which are not rank-one Abelian. Finally, we apply our methods to the case of braid...
On the dynamics of pseudo-Anosov homeomorphisms on representation varieties of surface groups.
On the embedding of coverings into 1-dimensional bundles.
On the essential height of homotopy trees with finite fundamental group
On the existence of universal covering spaces for metric spaces and subsets of the Euclidean plane
We prove several results concerning the existence of universal covering spaces for separable metric spaces. To begin, we define several homotopy-theoretic conditions which we then prove are equivalent to the existence of a universal covering space. We use these equivalences to prove that every connected, locally path connected separable metric space whose fundamental group is a free group admits a universal covering space. As an application of these results, we prove the main result of this article,...
On the Farrell cohomology of mapping class groups.
On the Finiteness Obstruction of Nilpotent Spaces of the Same Genus.