notes:2022-10-25-mina-aganagic-categorification-of-knot
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+ | ====== 2022-10-25, Mina Aganagic, categorification of knot ====== | ||
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+ | Talk at MSRI gauge theory workshop. | ||
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+ | ==== Khovanov homology and Jones polynomial ==== | ||
+ | Given a knot or link in $\R^3$, Jones produces a 1-variable polynomial $J_K(q)$. | ||
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+ | Khovanov upgraded that polynomial to a bi-graded vector space, and taking Euler characteristics in one grading, put formal variable $q$ in the other grading, recovers Jones polynomial. The construction is very much functorial, compatible with knot cobordism. | ||
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+ | Knot categorification is about constructing maps from the category of colored points on a surface with morphism being merge and isotopy, to the category of representation of quantum groups $U_q(g)$. | ||
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+ | Webster already did this categorification. Here Mina gives a physics and A-model explanation why Webster' | ||
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+ | This talk will not be about super Lie-algebra, | ||
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+ | ** Why we have quantum group ** | ||
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+ | In 88Witten, Chern-Simon, | ||
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+ | Conformal blocks, solutions to KZ equations | ||
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