Title: "Polar homology"

Abstract:

Polar homology groups arise as holomorphic analogs of singular

homology groups in topology. Polar chains in a complex projective manifold

are complex subvarieties with meromorphic forms on them, while the

boundary operator is defined by taking the divisor of poles and the

Poincare residue on the divisor. Similarly, one can define, e.g.,

holomorphic analogs of the Gauss linking number or symplectic structure

on moduli spaces of flat connections on a Riemann surface.