Researcher
Institut
Fourier, UMR 5582 du CNRS
Université de Grenoble I
BP 74, 38402 Saint-Martin d'Hères cedex, France
Office 329
Tel. : 33.4.76.63.56.16
Fax : 33.4.76.51.44.78
E-mail : lescop(I am sure you guess
what)fourier.ujf-grenoble.fr
Research
I
am mainly interested by 3-dimensional topology and knot
theory.
Here are a very introductory presentation of part of
my work Quelques
présentations des variétés de dimension 3
(in french) and a slightly less introductory survey of my results On
the Casson invariant..
I am currently mainly interested by finite type invariants of knots and 3-manifolds. The universal web reference for them is Dror Bar-Natan's homepage . Here is the program of the Institut Fourier Summer School that I organized in 1999 with lecture notes and links to the speaker homepages and here are my own introductory lecture notes on the Kontsevich integral that is together with the Configuration Space Integrals described in an introductory survey, in the lecture notes of a course I gave in Villa de Leyva (Columbia), and more completely in Sylvain Poirier's thesis one of the two (possibly equal) main universal real finite type knot invariants. My preprint About the uniqueness and the denominators of the Kontsevich integral specifies the relationship between these two invariants.
In the case of 3-manifolds, there are also two possibly equal universal real finite type invariants of integral homology spheres, the LMO invariant of Le, Murakami and Ohtsuki, and a configuration-space invariant. I described the beautiful topological construction of this latter invariant Z here in a detailed self-contained way, following the approach of Maxim Kontsevich, Greg Kuperberg and Dylan Thurston. I also proved splitting formulae for Z that generalize a property proved by Kuperberg and Thurston in order to show that Z is a universal finite-type invariant of integral homology 3-spheres. I applied these splitting formulae to prove various surgery formulae for finite type invariants of homology spheres and I applied these latter formulae to give a topological description of the third coefficient of the Jones polynomial of genus one knots.
Preprints, lecture notes, publication
list, and beamer talks.
Here are two photographs of myself (CIRM, November 2008), thanks to Michèle Audin. You can also look at my daughter Gaëlle and my son Ronan!
