Geography of bilinearized Legendrian contact homology

Abstract

We study the geography of bilinearized Legendrian contact homology for closed, connected Legendrian submanifolds with vanishing Maslov class in 1-jet spaces. We show that this invariant detects whether the two augmentations used to define it are DGA homotopic or not. We describe a collection of graded vector spaces containing all possible values for bilinearized Legendrian contact homology and then show that all these vector spaces can be realized.

39 pages, 11 figures; corrected definition of admissible bLCH polynomial, added a new construction at the end of the paper, added some details in several proofs, various minor corrections

References in corpus (3)

• Lagrangian Cobordisms via Generating Families: Constructions and Geography
• Augmentations are Sheaves
• Equivalence classes of augmentations and Morse complex sequences of Legendrian knots