Abstract
Using the diagrammatic calculus for Soergel bimodules, developed by Elias and Khovanov, as well as Rasmussen's spectral sequence, we construct an integral version of HOMFLY-PT and -link homology.
Highlights
During the past half-decade, categorification and, in particular, that of topological invariants has flourished into a subject of its own right
With a construction that utilized matrix factorizations, a tool previously developed in an algebra-geometric context, Khovanov and Rozansky produced the sl n and HOMFLY-PT link homology theories
The most insightful and influential work in uncovering these innerconnections was that of Rasmussen in 2, where he constructed a spectral sequence from the HOMFLY-PT to the sl n -link homology
Summary
During the past half-decade, categorification and, in particular, that of topological invariants has flourished into a subject of its own right. The organization of the paper is the following: in Section 2, we give a brief account of the necessary tools matrix factorizations, Soergel bimodules, Hochschild homology, Rouquier complexes, and corresponding diagrammatics —the emphasis here is brevity and we refer the reader to more original sources for particulars and details; in Sections 3 and 4, we describe the integral HOMFLY-PT complex and prove the Reidemeister moves, utilizing all of the background in Section 2; Section 5 is devoted to the Rasmussen spectral sequence and integral sl n -link homology We conclude it with some remarks and questions.
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