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# Documents  Kitano, Teruaki | enregistrements trouvés : 5

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## Differential equation for the Reidemeister torsion Marché, Julien | CIRM H

Post-edited

Research talks;Geometry;Topology

The Reidemeister torsion may be viewed as a volume form on the character variety of a 3-manifold with boundary. I will explain a conjectural differential equation that this form should satisfy, motivated by the study of the asymptotical behaviour of quantum invariants.

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## Finite type invariants of knots in homology 3-spheres Moussard, Delphine | CIRM H

Multi angle

Research talks;Topology

For null-homologous knots in rational homology 3-spheres, there are two equivariant invariants obtained by universal constructions à la Kontsevich, one due to Kricker and defined as a lift of the Kontsevich integral, and the other constructed by Lescop by means of integrals in configuration spaces. In order to explicit their universality properties and to compare them, we study a theory of finite type invariants of null-homologous knots in rational homology 3-spheres. We give a partial combinatorial description of the space of finite type invariants, graded by the degree. This description is complete for knots with a trivial Alexander polynomial, providing explicit universality properties for the Kricker lift and the Lescop equivariant invariant and proving the equivalence of these two invariants for such knots. For null-homologous knots in rational homology 3-spheres, there are two equivariant invariants obtained by universal constructions à la Kontsevich, one due to Kricker and defined as a lift of the Kontsevich integral, and the other constructed by Lescop by means of integrals in configuration spaces. In order to explicit their universality properties and to compare them, we study a theory of finite type invariants of null-homologous knots in ...

57M27

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## Equidistribution of square-tiled surfaces, meanders, and Masur-Veech volumes Zorich, Anton | CIRM H

Multi angle

Research talks;Combinatorics;Dynamical Systems and Ordinary Differential Equations;Topology

We show how recent results of the authors on equidistribution of square-tiled surfaces of given combinatorial type allow to compute approximate values of Masur-Veech volumes of the strata in the moduli spaces of Abelian and quadratic differentials by Monte Carlo method.
We also show how similar approach allows to count asymptotical number of meanders of fixed combinatorial type in various settings in all genera. Our formulae are particularly efficient for classical meanders in genus zero.
We construct a bridge between flat and hyperbolic worlds giving a formula for the Masur-Veech volume of the moduli space of quadratic differentials in terms of intersection numbers of $\mathcal{M}_{g,n}$ (in the spirit of Mirzakhani's formula for Weil-Peterson volume of the moduli space of pointed curves).
Joint work with V. Delecroix, E. Goujard, P. Zograf.
We show how recent results of the authors on equidistribution of square-tiled surfaces of given combinatorial type allow to compute approximate values of Masur-Veech volumes of the strata in the moduli spaces of Abelian and quadratic differentials by Monte Carlo method.
We also show how similar approach allows to count asymptotical number of meanders of fixed combinatorial type in various settings in all genera. Our formulae ...

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## L-space knots in twist families and satellite L-space knots Motegi, Kimihiko | CIRM H

Multi angle

Research talks;Topology

Twisting a knot $K$ in $S^3$ along a disjoint unknot $c$ produces a twist family of knots $\{K_n\}$ indexed by the integers. Comparing the behaviors of the Seifert genus $g(K_n)$ and the slice genus $g_4(K_n)$ under twistings, we prove that if $g(K_n) - g_4(K_n) < C$ for some constant $C$ for infinitely many integers $n > 0$ or $g(K_n) / g_4(K_n) \to 1$ as $n \to \infty$, then either the winding number of $K$ about $c$ is zero or the winding number equals the wrapping number. As an application, if $\{K_n\}$ contains infinitely many L-space knots, then the latter must occur. We further develop this to show that if $K_n$ is an L-space knot for infinitely many integers $n > 0$ and infinitely many integers $n < 0$, then $c$ is a braid axis. We then use this to show that satellite L-space knots are braided satellites.
This is joint work with Ken Baker.
Twisting a knot $K$ in $S^3$ along a disjoint unknot $c$ produces a twist family of knots $\{K_n\}$ indexed by the integers. Comparing the behaviors of the Seifert genus $g(K_n)$ and the slice genus $g_4(K_n)$ under twistings, we prove that if $g(K_n) - g_4(K_n) 0$ or $g(K_n) / g_4(K_n) \to 1$ as $n \to \infty$, then either the winding number of $K$ about $c$ is zero or the winding number equals the wrapping number. As an application, if \$\{K_...

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## Groups of diffeomorphisms:in honor of Shigeyuki Morita on the occasion of his 60th birthday Penner, Robert ; Kotschick, Dieter ; Tsuboi, Takashi ; Kawazumi, Nariya ; Kitano, Teruaki ; Mitsumatsu, Yoshihiko | Mathematical Society of Japan 2008

Ouvrage

- 524 p.
ISBN 978-4-931469-48-8

Advanced studies in pure mathematics , 0052

Localisation : Collection 1er étage

géométrie différentielle # groupe de difféomorphisme

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##### Codes MSC

Ressources Electroniques (Depuis le CIRM)

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