Acta Mathematica

The homotopy type of the cobordism category

Søren Galatius, Ib Madsen, Ulrike Tillmann, and Michael Weiss

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Abstract

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].

Note

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.

Article information

Source
Acta Math., Volume 202, Number 2 (2009), 195-239.

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

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485892397

Digital Object Identifier
doi:10.1007/s11511-009-0036-9

Mathematical Reviews number (MathSciNet)
MR2506750

Zentralblatt MATH identifier
1221.57039

Rights
2009 © Institut Mittag-Leffler

Citation

Galatius, Søren; Madsen, Ib; Tillmann, Ulrike; Weiss, Michael. The homotopy type of the cobordism category. Acta Math. 202 (2009), no. 2, 195--239. doi:10.1007/s11511-009-0036-9. https://projecteuclid.org/euclid.acta/1485892397


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