The homotopy type of the topological cobordism category
The homotopy type of the topological cobordism category
We define a cobordism category of topological manifolds and prove that if d\neq 4 its classifying space is weakly equivalent to \Omega^{\infty -1}MT\mathrm{Top}(d) , where MT\mathrm{Top}(d) is the Thom spectrum of the inverse of the canonical bundle over B\mathrm{Top}(d) . We also give versions for manifolds with tangential structures and/or …