15 February 2005 Categorification of the Temperley-Lieb category, tangles, and cobordisms via projective functors
Catharina Stroppel
Duke Math. J. 126(3): 547-596 (15 February 2005). DOI: 10.1215/S0012-7094-04-12634-X


To each generic tangle projection from the three-dimensional real vector space onto the plane, we associate a derived endofunctor on a graded parabolic version of the Bernstein-Gel'fand category $\mathcal{O}$. We show that this assignment is (up to shifts) invariant under tangle isotopies and Reidemeister moves and defines therefore invariants of tangles. The occurring functors are defined via so-called projective functors. The first part of the paper deals with the indecomposability of such functors and their connection with generalised Temperley-Lieb algebras which are known to have a realisation via decorated tangles. The second part of the paper describes a categorification of the Temperley-Lieb category and proves the main conjectures of [BFK]. Moreover, we describe a functor from the category of 2-cobordisms into a category of projective functors.


Download Citation

Catharina Stroppel. "Categorification of the Temperley-Lieb category, tangles, and cobordisms via projective functors." Duke Math. J. 126 (3) 547 - 596, 15 February 2005. https://doi.org/10.1215/S0012-7094-04-12634-X


Published: 15 February 2005
First available in Project Euclid: 11 February 2005

zbMATH: 1112.17010
MathSciNet: MR2120117
Digital Object Identifier: 10.1215/S0012-7094-04-12634-X

Rights: Copyright © 2005 Duke University Press


This article is only available to subscribers.
It is not available for individual sale.

Vol.126 • No. 3 • 15 February 2005
Back to Top