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Knot invariants via algebraic geometry


Speaker: Sabin Cautis, MSRI
Location: 1147 MSB
Start time: Mon, Jan 5 2009, 4:10PM

We explain how to construct knot and tangle invariants (such as Khovanov homology) by studying holomorphic vector bundles on certain compact, complex manifolds. Topologically these complex manifolds are just products of the same projective space P1. Conjecturially, if one used Grassmannians Gr(k,n) instead of projective spaces this would give a series of new knot invariants analogous to Khovanov homology (this is joint work with Joel Kamnitzer)