Séminaire Physique mathématique ICJ

Deligne-Beilinson cohomology in U(1) Chern-Simons and BF theories: an example of the Atiyah-Segal program

by Frank Thuillier (LAPTh)

Fokko du Cloux (Institut Camille Jordan)

Fokko du Cloux

Institut Camille Jordan

Université Lyon 1, Bât. Braconnier, 21 av. Claude Bernard, 69100 Villeurbanne
Deligne-Beilinson cohomology is a particularly efficient tool for the study of U(1) Chern-Simons and BF theories in the functional integration context of Quantum Field Theory. Its use yields Reshethikin-Turaev and Turaev-Viro invariants. In the BF case, a new set of surgery type formulas can be exhibited which are also related with an abelian version of Turaev-Virelizier theorem. Eventually, this cohomological approach to these topological theories provide an example of Atiyah-Segal program.