**Vladimir Sharafutdinov
Sobolev Institute of Mathematics, Russia, and UW**

*Date:* October 12, 2005

For a compact Riemannian manifold with boundary we define the
Dirichlet to Neumann (DN) operator on forms of arbitrary degree. It
coincides with the classical DN map on forms of degree zero. The
question we address is how much of the topology of the manifold can be
determined by knowing only the boundary of the manifold and the DN
operator? We show that we can determine the Betti numbers from this
information.