Equivariant orientation theory.

Costenoble, S.R.; May, J.P.; Waner, S.

Displaying similar documents to “Equivariant orientation theory.”

A higher dimensional homotopy sequence.

Grandis, M., Vitale, E.M. (2002)

Homology, Homotopy and Applications

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State spaces and dipaths up to dihomotopy.

Raussen, Martin (2003)

Homology, Homotopy and Applications

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Classifying toposes and foliations

Ieke Moerdijk (1991)

Annales de l'institut Fourier

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For any etale topological groupoid $G$ (for example, the holonomy groupoid of a foliation), it is shown that its classifying topos is homotopy equivalent to its classifying space. As an application, we prove that the fundamental group of Haefliger for the (leaf space of) a foliation agrees with the one introduced by Van Est. We also give a new proof of Segal’s theorem on Haefliger’s classifying space $B Γ^{q}$ .

The Mumford conjecture

Geoffrey Powell (2004-2005)

Séminaire Bourbaki

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The Mumford Conjecture asserts that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra on the Mumford-Morita-Miller characteristic classes; this can be reformulated in terms of the classifying space $B Γ_{\infty}$ derived from the mapping class groups. The conjecture admits a topological generalization, inspired by Tillmann’s theorem that $B Γ_{\infty}$ admits an infinite loop space structure after applying Quillen’s plus construction. The text presents the proof by...