Obstructions to Lagrangian Cobordisms between Legendrian Submanifolds

Details Obstructions to Lagrangian Cobordisms between Legendrian Submanifolds Obstructions to Lagrangian Cobordisms between Legendrian Submanifolds

2011-09-26

arxiv.org/abs/1109.5660v2

Mathematics

Symplectic Geometry

56 pages, 10 figures; small corrections to Corollary 1.2 and several examples in this version

Scientific paper

The technique of generating families produces obstructions to the existence of embedded Lagrangian cobordisms between Legendrian submanifolds in the symplectizations of 1-jet bundles. In fact, generating families may be used to construct a TQFT-like theory that, in addition to giving the aforementioned obstructions, yield structural information about invariants of Legendrian submanifolds. For example, the obstructions devised in this paper show that there is no generating family compatible Lagrangian cobordism between the Chekanov-Eliashberg Legendrian $m(5_2)$ knots. Further, the generating family cohomology groups of a Legendrian submanifold restrict the topology of a null-cobordism. Structurally, the generating family cohomology of a Legendrian submanifold satisfies a type of Alexander duality that, when the Legendrian is null-cobordant, can be seen as Poincar\'e duality of the associated Lagrangian null-cobordism. This duality implies the Arnold Conjecture for Legendrian submanifolds with linear-at-infinity generating families. The results are obtained by developing a generating family version of wrapped Floer cohomology and establishing long exact sequences that arise from viewing the the spaces underlying these cohomology groups as mapping cones.

Affiliated with

Also associated with

No associations

Rating

Obstructions to Lagrangian Cobordisms between Legendrian Submanifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Obstructions to Lagrangian Cobordisms between Legendrian Submanifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Obstructions to Lagrangian Cobordisms between Legendrian Submanifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-690122