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- W2964204244 abstract "It is known that knot homologies admit a physical description as spaces of open BPS states. We study operators and algebras acting on these spaces. This leads to a very rich story, which involves wall crossingphenomena, algebras of closed BPS states acting on spaces of open BPS states, and deformations of Landau-Ginzburg models.One important application to knot homologies is the existence of differentials that relate homological invariants of knots colored by differentrepresentations. Based on this structure, we formulate a list of properties of the colored HOMFLY homology that categorifies the colored HOMFLY polynomial. By calculating the colored HOMFLY homology for symmetric and anti-symmetric representations, we find a remarkable mirror symmetry between these triply-graded theories." @default.
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- W2964204244 date "2012-01-01" @default.
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- W2964204244 title "Homological algebra of knots and BPS states" @default.
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