The homotopy type of the cobordism category
http://jp.arxiv.org/abs/math/0605249
For d=2, our results lead to a new proof of the generalized Mumford conjecture, somewhat different in spirit from the original one.
http://jp.arxiv.org/abs/math/0605249
For d=2, our results lead to a new proof of the generalized Mumford conjecture, somewhat different in spirit from the original one.