An exceptional collection for Khovanov homology

Cooper, Benjamin¹ ; Hogancamp, Matt²

¹Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, 52242-1419, USA
²Department of Mathematics, Indiana University Bloomington, Rawles Hall, 831 E 3rd St, Bloomington, IN 47405, USA

Algebraic and Geometric Topology, Tome 15 (2015) no. 5, pp. 2659-2706

Résumé

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.

Détail

DOI : 10.2140/agt.2015.15.2659

Classification : 57R56, 57M27
Keywords: Jones–Wenzl projector, Temperley–Lieb, categorification

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