2013/06/30 by Varghese Mathai, Jonathan Rosenberg · 9 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Characteristic class #Cohomology #Computer science #Cover (algebra) #Duality (order theory) #Geometry #Homotopy #Homotopy and Cohomology in Algebraic Topology #K-theory (physics) #Mathematics #Noncommutative geometry #Pure mathematics #Section (typography) #hep-th #math.KT #math.OA
paper · pdf · doi:10.4310/atmp.2014.v18.n6.a6
published in Advances in Theoretical and Mathematical Physics 18(6), 1437-1462 · 19 pages, minor corrections including typo fixes and added references
openalex publication_date 2014/01/01 · arxiv created 2014/01/31 · arxiv updated 2014/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Recently Baraglia showed how topological T-duality can be extended to apply not only to principal circle bundles, but also to non-principal circle bundles. We show that his results can also be recovered via two other methods: the homotopy-theoretic approach of Bunke and Schick, and the noncommutative geometry approach which we previously used for principal torus bundles. This work has several interesting byproducts, including a study of the Ktheory of crossed products by O(2) = Isom(R), the universal cover of O( In the final section of this paper, some of these results are extended to the case of bundles with singular fibers, or in other words, non-free O(2)-actions.