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2009 The homotopy type of the cobordism category
Søren Galatius, Ib Madsen, Ulrike Tillmann, Michael Weiss
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Acta Math. 202(2): 195-239 (2009). DOI: 10.1007/s11511-009-0036-9


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].

Funding Statement

S. Galatius was partially supported by NSF grant DMS-0505740 and the Clay Institute.
M. Weiss was partially supported by the Royal Society and the Mittag-Leffler Institute.


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Søren Galatius. Ib Madsen. Ulrike Tillmann. Michael Weiss. "The homotopy type of the cobordism category." Acta Math. 202 (2) 195 - 239, 2009.


Received: 30 April 2007; Revised: 30 September 2008; Published: 2009
First available in Project Euclid: 31 January 2017

zbMATH: 1221.57039
MathSciNet: MR2506750
Digital Object Identifier: 10.1007/s11511-009-0036-9

Rights: 2009 © Institut Mittag-Leffler

Vol.202 • No. 2 • 2009
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