Fillable Contact Structures From Positive Surgery

Explore a comprehensive lecture on fillable contact structures resulting from positive surgery, delivered by Tom Mark from the University of Virginia at the Gauge Theory and Low Dimensional Topology conference. Delve into the necessary and sufficient conditions for contact n-surgery along a Legendrian knot to produce weakly symplectically fillable contact manifolds. Examine the specialized criteria for fillable positive surgery in the standard 3-sphere, including various obstructions and effective determination methods for knots up to 10 crossings. Investigate the topological implications, such as the relationship between lens space surgery and slice genus in knots. Gain insights into the proof's general approach, time permitting, while focusing primarily on the topological aspects of this fascinating subject in low-dimensional topology and contact geometry.