Arnold's seminar, Moscow, May 23, 2000

Polar homology and holomorphic linking number
Boris Khesin

Abstract

This is a joint work with Alexei Rosly (ITEPh).
For complex quasi-projective manifolds
we introduce polar homology groups, which are
holomorphic analogues of the homology groups in topology.
The polar $k$-chains are subvarieties of complex
dimension $k$ with meromorphic forms on them,
while the boundary operator is defined by
taking the polar divisor and the Poincar\'e
residue on it. We prove that Zariski open sets obey
the Mayer--Vietoris property. We also describe holomorphic 
versions of the intersection and linking numbers for complex 
submanifolds.