Knot Homology via Derived Categories of Coherent Sheaves I, Sl(2) Case
نویسندگان
چکیده
Using derived categories of equivariant coherent sheaves, we construct a categorification of the tangle calculus associated to sl(2) and its standard representation. Our construction is related to that of Seidel-Smith by homological mirror symmetry. We show that the resulting doubly graded knot homology agrees with Khovanov homology.
منابع مشابه
KNOT HOMOLOGY VIA DERIVED CATEGORIES OF COHERENT SHEAVES II, sl(m) CASE
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 mirr...
متن کاملKnot Homology via Derived Categories of Coherent Sheaves
Using derived categories of equivariant coherent sheaves, we construct a categorification of the tangle calculus associated to sl(2) and its standard representation. Our construction is related to that of Seidel-Smith by homological mirror symmetry. We show that the resulting doubly graded knot homology agrees with Khovanov homology.
متن کاملar 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
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 mirr...
متن کاملDERIVED EQUIVALENCES FOR COTANGENT BUNDLES OF GRASSMANNIANS VIA CATEGORICAL sl2 ACTIONS
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.
متن کاملar X iv : 0 90 2 . 17 97 v 2 [ m at h . A G ] 1 9 N ov 2 00 9 DERIVED EQUIVALENCES FOR COTANGENT BUNDLES OF GRASSMANNIANS VIA CATEGORICAL sl 2 ACTIONS
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.
متن کامل