Stable Pairs and Principal Bundles

2000 ◽  
Vol 51 (4) ◽  
pp. 417-436 ◽  
Author(s):  
D. Banfield
Keyword(s):  
Principal Bundles ◽  
Stable Pairs

scholarly journals Two-Categorical Bundles and their Classifying Spaces

2012 ◽  
Vol 10 (2) ◽  
pp. 299-369 ◽  
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.

scholarly journals Double principal bundles

2021 ◽  
pp. 104354
Author(s):  
Honglei Lang ◽  
Yanpeng Li ◽  
Zhangju Liu
Keyword(s):  
Principal Bundles

scholarly journals Mukai-Sakai bound for equivariant principal bundles

2005 ◽  
Vol 43 (1) ◽  
pp. 133-141
Author(s):  
Usha N. Bhosle ◽  
Indranil Biswas
Keyword(s):  
Principal Bundles

scholarly journals Criterion for connections on principal bundles over a pointed Riemann surface

2017 ◽  
Vol 4 (1) ◽  
pp. 155-171 ◽  
Author(s):  
Indranil Biswas
Keyword(s):  
Riemann Surface ◽  
Principal Bundles ◽  
Connections On Principal Bundles

Abstract We investigate connections, and more generally logarithmic connections, on holomorphic principal bundles over a compact connected Riemann surface.

scholarly journals Deformation quantization of principal bundles

2016 ◽  
Vol 13 (08) ◽  
pp. 1630010
Author(s):  
Paolo Aschieri
Keyword(s):  
Quantum Group ◽  
Deformation Quantization ◽  
Principal Bundle ◽  
Base Space ◽  
Structure Group ◽  
Galois Extensions ◽  
Principal Bundles ◽  
Group Of Automorphisms ◽  
Drinfeld Twist

We outline how Drinfeld twist deformation techniques can be applied to the deformation quantization of principal bundles into noncommutative principal bundles and, more in general, to the deformation of Hopf–Galois extensions. First, we twist deform the structure group in a quantum group, and this leads to a deformation of the fibers of the principal bundle. Next, we twist deform a subgroup of the group of automorphisms of the principal bundle, and this leads to a noncommutative base space. Considering both deformations, we obtain noncommutative principal bundles with noncommutative fiber and base space as well.

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