CIRM - Videos & books Library

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Left-handed flows are 3-dimensional flows which have a particular topological property, namely that every pair of periodic orbits is negatively linked. This property (introduced by Ghys in 2007) implies the existence of as many Bikrhoff sections as possible, and therefore allows to reduce the flow to a suspension in many different ways. It then becomes natural to look for examples. A construction of Birkhoff (1917) suggests that geodesic flows are good candidates. In this conference we determine on which hyperbolic orbifolds is the geodesic flow left-handed: the answer is that yes if the surface is a sphere with three cone points, and no otherwise.
dynamical system - geodesic flow - knot - periodic orbit - global section - linking number - fibered knot[-]

Left-handed flows are 3-dimensional flows which have a particular topological property, namely that every pair of periodic orbits is negatively linked. This property (introduced by Ghys in 2007) implies the existence of as many Bikrhoff sections as possible, and therefore allows to reduce the flow to a suspension in many different ways. It then becomes natural to look for examples. A construction of Birkhoff (1917) suggests that geodesic flows ...[+]

37C27 ; 37C15 ; 37C10 ; 57M25

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

In '84, Hirzebruch constructed a very explicit noncompact ball quotient manifold in the process of constructing smooth projective surfaces with Chern slope arbitrarily close to 3. I will discuss how this and some closely related ball quotients are useful in answering a variety of other questions. Some of this is joint with Luca Di Cerbo.

14M27 ; 32Q45 ; 57M50

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

An oriented manifold possesses an L-homology fundamental class which is an integral refinement of its Hirzebruch L-class and assembles to the symmetric signature. In joint work with Gerd Laures and James McClure, we give a construction of such an L-homology fundamental class for those oriented singular spaces, which are integral intersection homology Poincaré spaces. Our approach constructs a morphism of ad theories from intersection Poincaré bordism to L-theory. We shall indicate an application to the stratified Novikov conjecture. The latter has been treated analytically by Albin, Leichtnam, Mazzeo and Piazza.[-]

An oriented manifold possesses an L-homology fundamental class which is an integral refinement of its Hirzebruch L-class and assembles to the symmetric signature. In joint work with Gerd Laures and James McClure, we give a construction of such an L-homology fundamental class for those oriented singular spaces, which are integral intersection homology Poincaré spaces. Our approach constructs a morphism of ad theories from intersection Poincaré ...[+]

55N33 ; 57R67 ; 57R20 ; 57N80 ; 19G24

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

I will present the following results on real algebraic spatial curves:
(1) (joint with Mikhalkin) Classification of smooth irreducible spatial real algebraic curves of genus 0 or 1 up to degree 6 up to rigid isotopy.
(2) (joint with Mikhalkin) Classification of smooth irreducible spatial real algebraic curves with maximal encomplexed writhe up to (not rigid yet) isotopy.
(3) Classification of smooth spatial real algebraic curves of genus 0 with two irreducible components up to degree 6 up to rigid isotopy, in particular, the first (as far as know) example of two spatial real algebraic curves which are isotopic, have equal degree, genus and encomplexed writhe of each irreducible component but not rigidly isotopic.[-]

I will present the following results on real algebraic spatial curves:
(1) (joint with Mikhalkin) Classification of smooth irreducible spatial real algebraic curves of genus 0 or 1 up to degree 6 up to rigid isotopy.
(2) (joint with Mikhalkin) Classification of smooth irreducible spatial real algebraic curves with maximal encomplexed writhe up to (not rigid yet) isotopy.
(3) Classification of smooth spatial real algebraic curves of genus 0 with ...[+]

14P25

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

The local Gromov-Witten theory of curves studied by Bryan and Pandharipande revealed strong structural results for the local GW invariants, which were later used by Ionel and Parker in the proof of the Gopakumar-Vafa conjecture. In this talk I will report on a joint work in progress with Eleny Ionel on the extension of these results to the real setting.

14N35 ; 53D45

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

I will explain how to bound from above and below the expected Betti numbers of a random subcomplex in a simplicial complex and get asymptotic results under infinitely many barycentric subdivisions. This is a joint work with Nermin Salepci. It complements previous joint works with Damien Gayet on random topology.

52Cxx ; 60C05 ; 60B05 ; 55U10

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

We study a notion of shuffle for trees which extends the usual notion of a shuffle for two natural numbers. Our notion of shuffle is motivated by the theory of operads and occurs in the theory of dendroidal sets. We give several equivalent descriptions of the shuffles, and prove some algebraic and combinatorial properties. In addition, we characterize shuffles in terms of open sets in a topological space associated to a pair of trees. This is a joint work with Ieke Moerdijk.[-]

We study a notion of shuffle for trees which extends the usual notion of a shuffle for two natural numbers. Our notion of shuffle is motivated by the theory of operads and occurs in the theory of dendroidal sets. We give several equivalent descriptions of the shuffles, and prove some algebraic and combinatorial properties. In addition, we characterize shuffles in terms of open sets in a topological space associated to a pair of trees. This is a ...[+]

55U10 ; 18D50 ; 05C05

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

In the first part, we describe the canonical model structure on the category of strict $\omega$-categories and how it transfers to related subcategories. We then characterize the cofibrant objects as $\omega$-categories freely generated by polygraphs and introduce the key notion of polygraphic resolution. Finally, by considering a monoid as a particular $\omega$-category, this polygraphic point of view will lead us to an alternative definition of monoid homology, which happens to coincide with the usual one.[-]

In the first part, we describe the canonical model structure on the category of strict $\omega$-categories and how it transfers to related subcategories. We then characterize the cofibrant objects as $\omega$-categories freely generated by polygraphs and introduce the key notion of polygraphic resolution. Finally, by considering a monoid as a particular $\omega$-category, this polygraphic point of view will lead us to an alternative definition ...[+]

18D05 ; 18G55 ; 18G50 ; 18G10

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

The Toeplitz square peg problem asks if every simple closed curve in the plane inscribes a square. This is known for sufficiently regular curves (e.g. polygons), but is open in general. We show that the answer is affirmative if the curve consists of two Lipschitz graphs of constant less than 1 using an integration by parts technique, and give some related problems which look more tractable.

55N45

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

In these lectures, we will review what it means for a 3-manifold to have a hyperbolic structure, and give tools to show that a manifold is hyperbolic. We will also discuss how to decompose examples of 3-manifolds, such as knot complements, into simpler pieces. We give conditions that allow us to use these simpler pieces to determine information about the hyperbolic geometry of the original manifold. Most of the tools we present were developed in the 1970s, 80s, and 90s, but continue to have modern applications.[-]

In these lectures, we will review what it means for a 3-manifold to have a hyperbolic structure, and give tools to show that a manifold is hyperbolic. We will also discuss how to decompose examples of 3-manifolds, such as knot complements, into simpler pieces. We give conditions that allow us to use these simpler pieces to determine information about the hyperbolic geometry of the original manifold. Most of the tools we present were developed in ...[+]

57M27 ; 57M50 ; 57M25

Sélection Signaler une erreur

TUTELLES

PARTENAIRES

Destination de la recherche

Raccourcis

Topology 172 résultats

Which geodesic flows are left-handed? - Dehornoy, Pierre (Auteur de la Conférence) | CIRM H Nouveau

Variations on an example of Hirzebruch - Stover, Matthew (Auteur de la Conférence) | CIRM H Nouveau

The $\mathbb{L}^ \bullet$-Homology fundamental class for singular spaces and the stratified Novikov conjecture - Banagl, Markus (Auteur de la Conférence) | CIRM H Nouveau

On real algebraic knots and links - Orevkov, Stepan (Auteur de la Conférence) | CIRM H Nouveau

Real curves and a Klein TQFT - Georgieva, Penka (Auteur de la Conférence) | CIRM H Nouveau

Expected topology of a random subcomplex in a simplicial complex - Welschinger, Jean-Yves (Auteur de la Conférence) | CIRM H Nouveau

Shuffles of trees - Hoffbeck, Eric (Auteur de la Conférence) | CIRM H Nouveau

Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 1 - Métayer, François (Auteur de la Conférence) | CIRM H Nouveau

An integration approach to the Toeplitz square peg problem - Tao, Terence (Auteur de la Conférence) | CIRM H Nouveau

Structure of hyperbolic manifolds - Lecture 1 - Purcell, Jessica (Auteur de la Conférence) | CIRM H Nouveau