No abstract

No abstract

On a reduced analytic space X we introduce the concept of a generalized cycle, which extends the notion of a formal sum of analytic subspaces to include also a form part. We then consider a suitable equivalence relation and corresponding quotient B(X) that we think of as an analogue of the Chow group and a refinement of de Rham cohomology. This group allows us to study both global and local intersection theoretic properties.We provide many B-analogues of classical intersection theoretic constructions: For an analytic subspace V ⊂ X we define a B-Segre class, which is an element of B(X) with support in V . It satisfies a global King formula and, in particular, its multiplicities at each point coincide with the Segre numbers of V . When V is cut out by a section of a vector bundle we interpret this class as a Monge-Ampère-type product. For regular embeddings we construct a B-analogue of the Gysin morphism.