ar X iv : 0 71 0 . 32 16 v 2 [ m at h . A G ] 5 A pr 2 00 8 KNOT HOMOLOGY VIA DERIVED CATEGORIES OF COHERENT SHEAVES
نویسنده
چکیده
Using derived categories of equivariant coherent sheaves we construct a knot homology theory which categorifies the quantum sl(m) knot polynomial. Our knot homology naturally satisfies the categorified MOY relations and is conjecturally isomorphic to Khovanov-Rozansky homology. Our construction is motivated by the geometric Satake correspondence and is related to Manolescu’s by homological mirror symmetry.
منابع مشابه
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We construct an equivalence of categories from a strong categorical sl(2) action, following the work of Chuang-Rouquier. As an application, we give an explicit, natural equivalence between the derived categories of coherent sheaves on cotangent bundles to complementary Grassmannians.
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