The classifying space of the one-dimensional bordism category and a cobordism model for TC of spaces

摘要

The homotopy category of the bordism category hCd has as objects closed oriented (d-1)-manifolds and as morphisms diffeomorphism classes of d-dimensional bordisms. Using a new fiber sequence for bordism categories, we compute the classifying space of hCd for d=1, exhibiting it as a circle bundle over omega infinity-2CP-1 infinity.