HOMFLYPT homology for links in handlebodies via type A Soergel bimodules
David E.V. Rose, Daniel Tubbenhauer
TL;DR
This paper introduces a new triply-graded invariant for links in handlebodies, extending HOMFLYPT homology using braid group subgroups and Soergel bimodule categories, providing a novel algebraic framework for topological link invariants.
Contribution
It generalizes HOMFLYPT homology to links in handlebodies through categorical actions and Soergel bimodules, broadening the scope of link invariants in topology.
Findings
Defined a triply-graded invariant for links in handlebodies
Connected the invariant to categorical actions of Soergel bimodules
Extended the HOMFLYPT homology framework to new topological settings
Abstract
We define a triply-graded invariant of links in a genus g handlebody, generalizing the colored HOMFLYPT (co)homology of links in the 3-ball. Our main tools are the description of these links in terms of a subgroup of the classical braid group, and a family of categorical actions built from complexes of (singular) Soergel bimodules.
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