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Lectures on knot homology

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arxiv 1510.01795 v5 pith:XK2TPEC7 submitted 2015-10-07 math-ph hep-thmath.AGmath.GTmath.MPmath.RT

Lectures on knot homology

classification math-ph hep-thmath.AGmath.GTmath.MPmath.RT
keywords homologyknotformulationslecturesadditionalgebraiccentredualities
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We provide various formulations of knot homology that are predicted by string dualities. In addition, we also explain the rich algebraic structure of knot homology which can be understood in terms of geometric representation theory in these formulations. These notes are based on lectures in the workshop "Physics and Mathematics of Link Homology" at Centre de Recherches Mathematiques, Universite de Montreal.

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    This is a survey, not a new result: it reviews the q-series invariants Zhat, F_K, F_L and their supergroup analogues, collecting known conjectures, theorems, and examples.