Algebraic & Geometric Topology

An exceptional collection for Khovanov homology

Benjamin Cooper and Matt Hogancamp

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Jones–Wenzl projector Temperley–Lieb categorification


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.

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