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An infinite torus braid yields a categorified Jones-Wenzl projector

100%

Rozansky L.

Fundamenta Mathematicae

2014

tom 225

nr 1

305-326

A sequence of Temperley-Lieb algebra elements corresponding to torus braids with growing twisting numbers converges to the Jones-Wenzl projector. We show that a sequence of categorification complexes of these braids also has a limit which may serve as a categorification of the Jones-Wenzl projector.

Matrix factorizations and link homology

63%

Khovanov M., Rozansky L.

Fundamenta Mathematicae

2008

tom 199

nr 1

1-91

For each positive integer n the HOMFLYPT polynomial of links specializes to a one-variable polynomial that can be recovered from the representation theory of quantum sl(n). For each such n we build a doubly-graded homology theory of links with this polynomial as the Euler characteristic. The core of our construction utilizes the theory of matrix factorizations, which provide a linear algebra description of maximal Cohen-Macaulay modules on isolated hypersurface singularities.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Rozansky L.

1 Khovanov M.

1 2014

1 2008

Wyniki wyszukiwania

An infinite torus braid yields a categorified Jones-Wenzl projector

Matrix factorizations and link homology