Speaker
Description
A celebrated theorem of Ding and Geiges states that every connected, oriented, closed 3-manifold equipped with a cooriented contact structure can be obtained by contact surgery along a Legendrian link in the standard tight contact 3-sphere. This naturally leads to complexity measures for contact 3-manifolds: the contact surgery number and the contact surgery distance. The contact surgery distance between two contact 3-manifolds is the minimum number of contact surgeries required to pass from one to the other, while the contact surgery number of a contact 3-manifold is precisely its distance from the standard tight contact 3-sphere. In this talk, I will discuss joint work in which we compute contact surgery numbers for contact structures on the real projective 3-space and the 3-torus. If time permits, I will also discuss bounds on the contact surgery distance in terms of the corresponding smooth surgery distance.