The minimal length of a Lagrangian cobordism between Legendrians

Joshua M. Sabloff ^[1] ; Lisa Traynor ^[2]
1. [1] Haverford College
  
  Haverford College
  
  City of Philadelphia, Estados Unidos
2. [2] Bryn Mawr College
  
  Bryn Mawr College
  
  Township of Lower Merion, Estados Unidos
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 2, 2017, págs. 1419-1448
Idioma: inglés
Enlaces
- Texto completo
Resumen
- 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.