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We show an equivalence of infinite loop spaces between the classify- ing space of the cobordism category, with infinite loop space structure induced by taking disjoint union of manifolds, and the infinite loop space associated to the Madsen-Tillmann spectrum.
Categories and cohomology theories
Graeme Segal · 1974
Earlier work this paper cites.
A note on the spectra of algebraic K K -theory
Zbigniew Fiedorowicz · 1977
Earlier work this paper cites.
Homotopy theory of Γ \Gamma -spaces, spectra, and bisimplicial sets
A. K. Bousfield and E. M. Friedlander · 1978
Earlier work this paper cites.
The uniqueness of infinite loop space machines
J. P. May and R. Thomason · 1978
Earlier work this paper cites.
The stable mapping class group and Q ( ℂ P + ∞ ) Q(\mathbb{C}P^{\infty}_{+})
Ib Madsen and Ulrike Tillmann · 2001
Cited alongside, same era.
Model categories of diagram spectra
M. A. Mandell, J. P. May, S. Schwede, and B. Shipley · 2001
Cited alongside, same era.
The homotopy type of the cobordism category
Søren Galatius, Ulrike Tillmann, Ib Madsen, and Michael Weiss · 2009
Cited alongside, same era.
Monoids of moduli spaces of manifolds
Søren Galatius and Oscar Randal-Williams · 2010
Later among the works it cites.
Stable homology of automorphism groups of free groups
Søren Galatius · 2011
Later among the works it cites.
The cobordism category and Waldhausen’s K K -theory
Marcel Bökstedt and Ib Madsen · 2014
Later among the works it cites.
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