$SU(2)$ Chern-Simons invariant from Heegaard splitting

par Philippe Mathieu (LAPTh)

jeudi 7 sept. 2017, 11:00 → 12:00 Europe/Paris

Auditorium (Annecy-le-Vieux)

We introduce the so-called Heegaard splitting which is a particular decomposition of 3-manifolds in two identical handled bodies with a specific gluing rule. We show how such a symmetrical decomposition can be used to compute the Chern-Simons invariant for a given $SU(2)$ flat connection. More precisely, we will see that the Chern-Simons invariant, which is a volume term, can be rewritten as a sum of two surface terms, with at least one that can be determined graphically.