Residue currents and the Euler characteristic of a complex of vector bundles

I will describe a factorization of the fundamental cycle of a bounded
generically exact complex of vector bundles in terms of certain
differential forms and residue currents associated to this complex. This
is a generalization of previous results in the case when the complex is
a locally free resolution of the structure sheaf of an analytic space,
which in turn is a generalization of the Poincaré-Lelong formula. This
is joint work with Elizabeth Wulcan.