The homotopy type of the PL cobordism category, I

We introduce a bordism category Cob PL d whose objects are bundles of closed .d1/-dimensional piecewise linear manifolds and whose morphisms are bundles of d -dimensional piecewise linear cobordisms.In the main theorem, we show that the classifying space BCob PL d is weak homotopy equivalent to an infinite loop space.We regard Cob PL d as the piecewise linear analogue of the category of smooth cobordisms which has been studied extensively in connection with the Madsen-Weiss theorem, and our main result is a first step towards obtaining Madsen-Weiss type results in the context of PL topology.