Essential mappings onto products of manifolds
Birman and Menasco (1994) introduced and studied a class of embedded tori in closed braid complements which admit a standard tiling. The geometric description of the tori from this class was not complete. Ng showed (1988) that each essential torus in a closed braid complement which admits a standard tiling possesses a staircase tiling pattern. In this paper, we introduce and study the so-called longitude-meridional patterns for essential tori admitting a standard tiling. A longitude-meridional...
The states of the title are a set of knot types which suffice to create a generating set for the Kauffman bracket skein module of a manifold. The minimum number of states is a topological invariant, but quite difficult to compute. In this paper we show that a set of states determines a generating set for the ring of characters of the fundamental group, which in turn provides estimates of the invariant.
Dans cet article, on montre que l’espace des groupes marqués est un sous-espace fermé d’un ensemble de Cantor dont la dimension de Hausdorff est infinie. On prouve que la dimension de Minkowski de cet espace est infinie en exhibant des sous-ensembles de groupes marqués à petite simplification dont les dimensions de Minkowski sont arbitrairement grandes. On donne une estimation des dimensions de Minkowski de sous-espaces de groupes à un relateur. On démontre enfin que les dimensions de Minkowski...
Cet article contient une démonstration géométrique simple de pour .Ce résultat (démontré aussi par Mather comme corollaire d’un théorème beaucoup plus général) apparaît comme une conséquence du théorème de Michael Herman : .L’appendice contient une étude des structures sur les surfaces et un résultat sur la cohomologie de .
A certain p-th order cup product is detected by a p-th order cohomology operation. The result is applied to finite H-spaces, to show that several properties of compact Lie groups do not hold for arbitrary torsion free finite H-spaces.
A result by Dehornoy (1992) says that every nontrivial braid admits a -definite expression, defined as a braid word in which the generator with maximal index appears with exponents that are all positive, or all negative. This is the ground result for ordering braids. In this paper, we enhance this result and prove that every braid admits a -definite word expression that, in addition, is quasi-geodesic. This establishes a longstanding conjecture. Our proof uses the dual braid monoid and a new...