Towards flexibility for higher-dimensional contact manifolds

Geometry Topology Seminar
Monday, September 24, 2012 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Olga Plamenevskaya – SUNY - Stony Brook
John Etnyre
By a classical result of Eliashberg, contact manifolds in dimension 3 come in two flavors: tight (rigid) and overtwisted (flexible). Characterized by the presence of an "overtwisted disk", the overtwisted contact structures form a class where isotopy and homotopy classifications are equivalent.In higher dimensions, a class of flexible contact structures is yet to be found. However, some attempts to generalize the notion of an overtwisted disk have been made. One such object is a "plastikstufe" introduced by Niederkruger following some ideas of Gromov. We show that under certain conditions, non-isotopic contact structures become isotopic after connect-summing with a contact sphere containing a plastikstufe. This is a small step towards finding flexibility in higher dimensions. (Joint with E. Murphy, K. Niederkruger, and A. Stipsicz.)