Classifying Spaces | ScienceGate

LetBGbe the classifying space of a finite groupG. Consider the problem of finding astabledecompositionintoindecomposablewedge summands. Such a decomposition naturally splitsE*(BG), whereE* is any cohomology theory.

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Curvature of classifying spaces for Brieskorn lattices

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2008.07.008 ◽

2008 ◽

Vol 58 (11) ◽

pp. 1591-1606 ◽

Cited By ~ 5

Author(s):

Claus Hertling ◽

Christian Sevenheck

Keyword(s):

Classifying Spaces

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Spaces of maps into classifying spaces for equivariant crossed complexes

Indagationes Mathematicae ◽

10.1016/s0019-3577(97)89117-3 ◽

1997 ◽

Vol 8 (2) ◽

pp. 157-172 ◽

Cited By ~ 6

Author(s):

R. Brown ◽

M. Golasiński ◽

T. Porter ◽

A. Tonks

Keyword(s):

Classifying Spaces

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Two-Categorical Bundles and their Classifying Spaces

Journal of K-theory K-theory and its Applications to Algebra Geometry and Topology ◽

10.1017/is012001012jkt181 ◽

2012 ◽

Vol 10 (2) ◽

pp. 299-369 ◽

Cited By ~ 2

Author(s):

Nils A. Baas ◽

Marcel Bökstedt ◽

Tore August Kro

Keyword(s):

Vector Bundle ◽

Vector Bundles ◽

Vector Spaces ◽

Bundle Theory ◽

Classifying Spaces ◽

Classifying Space ◽

Principal Bundles

AbstractFor a 2-category 2C we associate a notion of a principal 2C-bundle. For the 2-category of 2-vector spaces, in the sense of M.M. Kapranov and V.A. Voevodsky, this gives the 2-vector bundles of N.A. Baas, B.I. Dundas and J. Rognes. Our main result says that the geometric nerve of a good 2-category is a classifying space for the associated principal 2-bundles. In the process of proving this we develop powerful machinery which may be useful in further studies of 2-categorical topology. As a corollary we get a new proof of the classification of principal bundles. Another 2-category of 2-vector spaces has been proposed by J.C. Baez and A.S. Crans. A calculation using our main theorem shows that in this case the theory of principal 2-bundles splits, up to concordance, as two copies of ordinary vector bundle theory. When 2C is a cobordism type 2-category we get a new notion of cobordism-bundles which turns out to be classified by the Madsen–Weiss spaces.

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