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Let $M$ be a surface, let $N$ be a subsurface, and let $n \leq m$ be two positive integers. The inclusion of $N$ in $M$ gives rise to a homomorphism from the braid group $B_{n} N$ with $n$ strings on $N$ to the braid group $B_{m} M$ with $m$ strings on $M$ . We first determine necessary and sufficient conditions that this homomorphism is injective, and we characterize the commensurator, the normalizer and the centralizer of $π_{1} N$ in $π_{1} M$ . Then we calculate the commensurator, the normalizer and the centralizer of $B_{n} N$ in $B_{m} M$ for large surface braid...

Geometric types of twisted knots

Mohamed Aït-Nouh, Daniel Matignon, Kimihiko Motegi (2006)

Annales mathématiques Blaise Pascal

Let $K$ be a knot in the $3$ -sphere $S^{3}$ , and $Δ$ a disk in $S^{3}$ meeting $K$ transversely in the interior. For non-triviality we assume that $| Δ \cap K | \geq 2$ over all isotopies of $K$ in $S^{3} - \partial Δ$ . Let $K_{Δ, n}$ ( $\subset S^{3}$ ) be a knot obtained from $K$ by $n$ twistings along the disk $Δ$ . If the original knot is unknotted in $S^{3}$ , we call $K_{Δ, n}$ a twisted knot. We describe for which pair $(K, Δ)$ and an integer $n$ , the twisted knot $K_{Δ, n}$ is a torus knot, a satellite knot or a hyperbolic knot.

Geometrically fibred two-knots.

J.A. Hillman, S.P. Plotnick (1990)

Mathematische Annalen

Géométrie réelle des dessins d’enfant

Layla Pharamond dit d’Costa (2004)

Journal de Théorie des Nombres de Bordeaux

À tout dessin d’enfant est associé un revêtement ramifié de la droite projective complexe $P_{ℂ}^{1}$ , non ramifié en dehors de 0, 1 et l’infini. Cet article a pour but de décrire la structure algébrique de l’image réciproque de la droite projective réelle par ce revêtement, en termes de la combinatoire du dessin d’enfant. Sont rappelées en annexe les propriétés de la restriction de Weil et des dessins d’enfants utilisées.

Géométries modèles de dimension trois

Yves de Cornulier (2008/2009)

Séminaire de théorie spectrale et géométrie

On expose une preuve détaillée de la classification par Thurston des huit géométries modèles de dimension trois.

Geometrization of three manifolds and Perelman's proof.

Joan Porti (2008)

RACSAM

This is a survey about Thurston’s geometrization conjecture of three manifolds and Perelman’s proof with the Ricci flow. In particular we review the essential contribution of Hamilton as well as some results in topology relevants for the proof.

Geometry and topology of $ℝ$ -covered foliations.

Calegari, Danny (2000)

Electronic Research Announcements of the American Mathematical Society [electronic only]

Geometry of fluid motion

Boris Khesin (2002/2003)

Séminaire Équations aux dérivées partielles

We survey two problems illustrating geometric-topological and Hamiltonian methods in fluid mechanics: energy relaxation of a magnetic field and conservation laws for ideal fluid motion. More details and results, as well as a guide to the literature on these topics can be found in [3].

Geometry of links.

Jablan, Slavik V. (1999)

Novi Sad Journal of Mathematics

Geometry of pseudocharacters.

Manning, Jason Fox (2005)

Geometry & Topology

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