Existence of generating families on Lagrangian cobordisms

Abstract

For an embedded exact Lagrangian cobordism between Legendrian submanifolds in the 1-jet bundle, we prove that a generating family linear at infinity on the Legendrian at the negative end extends to a generating family linear at infinity on the Lagrangian cobordism after stabilization if and only if the formal obstructions vanish. In particular, a Lagrangian filling with trivial stable Lagrangian Gauss map admits a generating family linear at infinity.

18 pages, 2 figure. Comments are welcome! v2: correction on Def 1.3. v3: major revisions; correction on Def 1.3 & 2.3, Lem 2.11 & 2.12 (previous Lem 2.10), revisions on Thm 2.16 (previous Thm 2.15), and expository revisions in Sec 2.1 & 2.4. To appear in Math. Ann