Symmetric topological complexity for finite spaces and classifying spaces

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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Topological complexity of frictional interfaces: friction networks

Nonlinear Processes in Geophysics ◽

10.5194/npg-19-215-2012 ◽

2012 ◽

Vol 19 (2) ◽

pp. 215-225 ◽

Cited By ~ 10

Author(s):

H. O. Ghaffari ◽

R. P. Young

Keyword(s):

Topological Complexity ◽

Type Ii ◽

Stored Energy ◽

Fracture Permeability ◽

Radiated Energy ◽

Universal Power Law ◽

Shear Rupture ◽

Crack Type ◽

Network Properties ◽

Highly Correlated

Abstract. Through research conducted in this study, a network approach to the correlation patterns of void spaces in rough fractures (crack type II) was developed. We characterized friction networks with several networks characteristics. The correlation among network properties with the fracture permeability is the result of friction networks. The revealed hubs in the complex aperture networks confirmed the importance of highly correlated groups to conduct the highlighted features of the dynamical aperture field. We found that there is a universal power law between the nodes' degree and motifs frequency (for triangles it reads T(k) &propto; kβ (β &approx; 2 ± 0.3)). The investigation of localization effects on eigenvectors shows a remarkable difference in parallel and perpendicular aperture patches. Furthermore, we estimate the rate of stored energy in asperities so that we found that the rate of radiated energy is higher in parallel friction networks than it is in transverse directions. The final part of our research highlights 4 point sub-graph distribution and its correlation with fluid flow. For shear rupture, we observed a similar trend in sub-graph distribution, resulting from parallel and transversal aperture profiles (a superfamily phenomenon).

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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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