Event № 902
Event № 902
TE Geometry and Topology Seminar - Jean-Mathieu Magot (Grenoble) 27/03/2014, Thursday, 15:45
Name: Geometry and Topology Seminar
Title: Splitting the Theta-invariant using finite type invariant theory and combinatorics.
Speaker: Jean-Mathieu Magot (Grenoble)
Place: Amado 919, Technion
In the nineties, M. Kontsevich defined an invariant Z of integral homology spheres equipped with a parallelization. This invariant is a graded object so that it makes sense to ask for a description of its lowest degree part, called the Theta-invariant. In 2000, G. Kuperberg and D. Thurston revisited the construction of Z and proved many of its properties. In particular they proved that Theta(M, tau) splits as the sum of 6 times the Casson invariant of M and 1/4 of the first relative Pontrjagin class. Later on, C. Lescop gave another construction of Z and proved that if M is a rational homology sphere and X a homotopy class of nowhere vanishing vector fields on M, then Theta(M, X) is defined and satisfies a relation as above and provides an invariant of nowhere vanishing vector fields. In this talk, I will present a purely combinatorial proof of the latter relation, using finite type invariant theory and C. Lescop's recent combinatorial formula for the Theta-invariant from Heegaard diagrams. All prerequisites will be reviewed.
SubmittedBy: Tobias Hartnick , firstname.lastname@example.org
EventLink: Event № 902