Apparaît dans la collection : Summer School 2015: Moduli Problems in Symplectic Geometry

Cylindrical contact homology is arguably one of the more notorious Floer-theoretic constructions. The past decade has been less than kind to this theory, as the growing knowledge of gaps in its foundations has tarnished its claim to being a well-defined contact invariant. However, jointly with Hutchings we have managed to redeem this theory in dimension 3 for dynamically convex contact manifolds. This talk will highlight our implementation of non-equivariant constructions, domain dependent almost complex structures, automatic transversality, and obstruction bundle gluing, yielding a homological contact invariant which is expected to be isomorphic to $SH^+$ under suitable assumptions, though it does not require a filling of the contact manifold. By making use of family Floer theory we obtain an $S^1$-equivariant theory defined over Z coefficients, which when tensored with Q yields cylindrical contact homology, now with the guarantee of well-definedness and invariance.