Algebraic & Geometric Topology

An exceptional collection for Khovanov homology

Benjamin Cooper and Matt Hogancamp

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Abstract

The Temperley–Lieb algebra is a fundamental component of SU(2) topological quantum field theories. We construct chain complexes corresponding to minimal idempotents in the Temperley–Lieb algebra. Our results apply to the framework which determines Khovanov homology. Consequences of our work include semi-orthogonal decompositions of categorifications of Temperley–Lieb algebras and Postnikov decompositions of all Khovanov tangle invariants.

Article information

Source
Algebr. Geom. Topol., Volume 15, Number 5 (2015), 2659-2706.

Dates
Received: 2 December 2013
Revised: 29 August 2014
Accepted: 30 November 2014
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841028

Digital Object Identifier
doi:10.2140/agt.2015.15.2659

Mathematical Reviews number (MathSciNet)
MR3426689

Zentralblatt MATH identifier
1348.57046

Subjects
Primary: 57R56: Topological quantum field theories
Secondary: 57M27: Invariants of knots and 3-manifolds

Keywords
Jones–Wenzl projector Temperley–Lieb categorification

Citation

Cooper, Benjamin; Hogancamp, Matt. An exceptional collection for Khovanov homology. Algebr. Geom. Topol. 15 (2015), no. 5, 2659--2706. doi:10.2140/agt.2015.15.2659. https://projecteuclid.org/euclid.agt/1510841028


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