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2017 The augmentation category map induced by exact Lagrangian cobordisms
Yu Pan
Algebr. Geom. Topol. 17(3): 1813-1870 (2017). DOI: 10.2140/agt.2017.17.1813

Abstract

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.

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Yu Pan. "The augmentation category map induced by exact Lagrangian cobordisms." Algebr. Geom. Topol. 17 (3) 1813 - 1870, 2017. https://doi.org/10.2140/agt.2017.17.1813

Information

Received: 1 August 2016; Revised: 21 December 2016; Accepted: 1 January 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06762602
MathSciNet: MR3677941
Digital Object Identifier: 10.2140/agt.2017.17.1813

Subjects:
Primary: 53D42, 57R17
Secondary: 53D12, 57M50

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 3 • 2017
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