Series: Mathematics Colloquium

Date: Thursday, February 19, 2004

Time: 4:00 - 5:00 PM

Place: 102 McAllister Building

Host: Alexander Nabutovsky

Refreshments: 3:15 - 4:00 PM, in 212 McAllister

Speaker: Boris Khesin, University of Toronto

Title: Holomorphic Linking Numbers

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 relation to the holomorphic
  Chern-Simons theory.