Fillable Contact Structures From Positive Surgery

This course explores the necessary and sufficient conditions for contact n-surgery along a Legendrian knot in a closed contact 3-manifold to yield a weakly symplectically fillable contact manifold. It provides an effective criterion for the existence of a fillable positive surgery, along with various obstructions, and determines the existence of such surgery for knots of up to 10 crossings. The course also discusses topological consequences, such as the relationship between lens space surgery and slice genus. The teaching method involves exploring topologically-flavored aspects with hints of the general proof if time allows. The intended audience includes individuals interested in gauge theory, low-dimensional topology, and contact structures.