| Date: Tuesday, December 02, 2008
Title: Holomorphic linking number and gauge theory
Abstract: The Gauss linking number of two curves in the three-space has
a complex counterpart. In the talk we define the holomorphic linking
number for complex curves in complex three-folds. Moreover, one can define
"polar homology" groups of complex projective manifolds by regarding
meromorphic forms on their submanifolds as a complex analogue of
orientation, and taking the residue as the boundary operator. We also
discuss gauge-theoretic aspects of the above correspondence, and, in
particular, its relations to the holomorphic Chern--Simons theory
and to the symplectic structures on moduli spaces of flat connections and
of holomorphic bundles over surfaces.
Speaker: Boris Khesin
Institution: University of Toronto
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