The augmentation category map induced by exact Lagrangian cobordisms

Pan, Yu

doi:10.2140/agt.2017.17.1813

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The augmentation category map induced by exact Lagrangian cobordisms

Yu Pan

Algebraic & Geometric Topology 17 (2017) 1813–1870

DOI: 10.2140/agt.2017.17.1813

Abstract

To a Legendrian knot, one can associate an $A_{\infty}$ 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.

Keywords

the augmentation category, Lagrangian cobordisms, wrapped Floer homology, Legendrian knots

Mathematical Subject Classification 2010

Primary: 53D42, 57R17

Secondary: 53D12, 57M50

References

Publication

Received: 1 August 2016

Revised: 21 December 2016

Accepted: 1 January 2017

Published: 17 July 2017

Authors

Yu Pan
Mathematics Department Duke University Durham, NC United States
http://sites.google.com/site/yupanduke/

Volume 17, issue 3 (2017)