Volume 15, issue 5 (2015)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
An exceptional collection for Khovanov homology

Benjamin Cooper and Matt Hogancamp

Algebraic & Geometric Topology 15 (2015) 2659–2706
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.

Keywords
Jones–Wenzl projector, Temperley–Lieb, categorification
Mathematical Subject Classification 2010
Primary: 57R56
Secondary: 57M27
References
Publication
Received: 2 December 2013
Revised: 29 August 2014
Accepted: 30 November 2014
Published: 10 December 2015
Authors
Benjamin Cooper
Department of Mathematics
University of Iowa
14 MacLean Hall
Iowa City, 52242-1419
USA
Matt Hogancamp
Department of Mathematics
Indiana University Bloomington
Rawles Hall
831 E 3rd St
Bloomington, IN 47405
USA