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Mathematics Colloquium

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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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