# 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].

## 133 Citations

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The main goal of the present thesis is an exposition of the BökstedtMadsen theorem ([BM]), which relates the classifying space of the embedded cobordism category to certain iterated loop spaces of…

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### The equivariant cobordism category

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