Tightness and Legendrian Surgery in Contact Structures

Explore a 52-minute conference talk delving into the relationship between contact structures and open book decompositions in three-manifolds. Discover Giroux's renowned result establishing a one-to-one correspondence between isotopy classes of contact structures and stabilization classes of open book decompositions. Learn about a new characterization of tightness for contact structures in terms of corresponding open book decompositions. Examine how this characterization can be applied to address the question of whether tightness is preserved under Legendrian surgery. Gain insights into the intersection of contact geometry and low-dimensional topology through this BIMSA-presented talk by Andy Wand at ICBS2024.