Links in genus-g handlebodies are assigned a triply-graded homology built from singular Soergel bimodules and Hochschild cohomology, generalizing colored HOMFLYPT homology.
The 1,2-coloured HOMFLY-PT link homology
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In this paper we define the 1,2-coloured HOMFLY-PT link homology and prove that it is a link invariant. We conjecture that this homology categorifies the coloured HOMFLY-PT polynomial for links whose components are labelled 1 or 2.
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HOMFLYPT homology for links in handlebodies via type A Soergel bimodules
Links in genus-g handlebodies are assigned a triply-graded homology built from singular Soergel bimodules and Hochschild cohomology, generalizing colored HOMFLYPT homology.