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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The augmentation category map induced by exact Lagrangian cobordisms

Yu Pan

Algebraic & Geometric Topology 17 (2017) 1813–1870

To a Legendrian knot, one can associate an A category, the augmentation category. An exact Lagrangian cobordism between two Legendrian knots gives a functor of the augmentation categories of the two knots. We study this functor and establish a long exact sequence relating the corresponding cohomology of morphisms of the two ends. As applications, we prove that the functor between augmentation categories is injective on the level of equivalence classes of objects and find new obstructions to the existence of exact Lagrangian cobordisms in terms of linearized contact homology and ruling polynomials.

the augmentation category, Lagrangian cobordisms, wrapped Floer homology, Legendrian knots
Mathematical Subject Classification 2010
Primary: 53D42, 57R17
Secondary: 53D12, 57M50
Received: 1 August 2016
Revised: 21 December 2016
Accepted: 1 January 2017
Published: 17 July 2017
Yu Pan
Mathematics Department
Duke University
Durham, NC
United States