Two-Categorical Bundles and Their Classifying Spaces
| dc.creator | Baas, Nils. A. | |
| dc.creator | Bokstedt, Marcel | |
| dc.creator | Kro, Tore August | |
| dc.date | 2006-12-19 | |
| dc.date | 2008-08-01 | |
| dc.date.accessioned | 2026-07-07T09:54:03Z | |
| dc.date.available | 2026-07-07T09:54:03Z | |
| dc.description | For a 2-category 2C we associate a notion of a principal 2C-bundle. In case of the 2-category of 2-vector spaces in the sense of M.M. Kapranov and V.A. Voevodsky this gives the 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 a lot of 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. A calculation based on the main theorem shows that the principal 2-bundles associated to the 2-category of 2-vector spaces in the sense of J.C. Baez and A.S. Crans split, up to concordance, as two copies of ordinary vector bundles. 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. | |
| dc.description | LaTex, 64 pages, revised version | |
| dc.identifier | https://arxiv.org/abs/math/0612549 | |
| dc.identifier | http://arxiv.org/abs/math/0612549 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166174 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Category Theory | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 55R65 (Primary) 18D05, 19D99 (Secondary) | |
| dc.title | Two-Categorical Bundles and Their Classifying Spaces | |
| dc.type | text |