All News

Journal Article: Professor of Mathematics Lisa Traynor

May 3, 2017

Authors: Sabloff, JM; Traynor, L

Source: SELECTA MATHEMATICA-NEW SERIES, 23 (2):1419-1448; 10.1007/s00029-016-0288-0 APR 2017 

Abstract:

To investigate the rigidity and flexibility of Lagrangian cobordisms between Legendrian submanifolds, we study the minimal length of such a cobordism, which is a 1-dimensional measurement of the non-cylindrical portion of the cobordism. Our primary tool is a set of real-valued capacities for a Legendrian submanifold, which are derived from a filtered version of Legendrian contact homology. Relationships between capacities of Legendrians at the ends of a Lagrangian cobordism yield lower bounds on the length of the cobordism. We apply the capacities to Lagrangian cobordisms realizing vertical dilations (which may be arbitrarily short) and contractions (whose lengths are bounded below). We also study the interaction between length and the linking of multiple cobordisms as well as the lengths of cobordisms derived from non-trivial loops of Legendrian isotopies.