  In this paper we study the topology of the cobordism category of open and
closed strings. This is a 2-category in which the objects are compact
one-manifolds whose boundary components are labeled by an indexing set (the set
of "D-branes"), the 1-morphisms are cobordisms of manifolds with boundary, and
the 2-morphisms are diffeomorphisms of the surface cobordisms. Our methods and
techniques are direct generalizations of those used by U. Tillmann in her study
of the category of closed strings. We input the striking theorem of Madsen and
Weiss regarding the topology of the stable mapping class group to identify the
homotopy type of the geometric realization of the category of open and closed
strings as an infinite loop space.
