Séminaires : Séminaire d'Algèbre

Equipe(s) : gr,
Responsables :J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud.
Email des responsables : Jacques Alev <jacques.alev@univ-reims.fr>, David Hernandez <david.hernandez@imj-prg.fr>, Bernhard Keller <bernhard.keller@imj-prg.fr>, Thierry Levasseur <Thierry.Levasseur@univ-brest.fr>, Sophie Morier-Genoud <sophie.morier-genoud@imj-prg.fr>
Salle : 001
Adresse :IHP


Orateur(s) Zhengfang WANG - Bonn,
Titre Gerstenhaber algebra structure on the Tate-Hochschild cohomology
Horaire14:00 à 15:00
RésumeThe Tate-Hochschild cohomology of a singular space X is defined as the graded endomorphism ring of the diagonal inside the singularity category of X x X. Singularity categories were introduced by Buchweitz in representation theory and then rediscovered by Orlov in algebraic geometry and homological mirror symmetry. By Keller's very recent result, the Tate-Hochschild cohomology of an algebra is isomorphic to the Hochschild cohomology of its dg singularity category. In this talk, we construct an explicit complex to compute the Tate-Hochschild cohomology. We prove that there is a natural action of the little 2-discs operad on this complex. In particular, the Tate-Hochschild cohomology is a Gerstenhaber algebra. We also talk about a joint work with M. Rivera that the Tate-Hochschild cohomology of a simply-connected manifold M recovers the Rabinowitz-Floer homology of the unit disc cotangent bundle on M.