The homotopy type of the cobordism category

@article{Galatius2006TheHT,
  title={The homotopy type of the cobordism category},
  author={S{\o}ren Galatius and Ib Henning Madsen and Ulrike Tillmann and Michael Weiss},
  journal={Acta Mathematica},
  year={2006},
  volume={202},
  pages={195-239}
}
The embedded cobordism category under study in this paper generalizes the category of conformal surfaces, introduced by G. Segal in [S2] in order to formalize the concept of field theories. Our main result identifies the homotopy type of the classifying space of the embedded d-dimensional cobordism category for all d. For d = 2, our results lead to a new proof of the generalized Mumford conjecture, somewhat different in spirit from the original one, presented in [MW]. 

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