Bunke, Ulrich; Rumpf, Philipp; Schick, Thomas The topology of T-duality for \(T^{n}\)-bundles. (English) Zbl 1116.55007 Rev. Math. Phys. 18, No. 10, 1103-1154 (2006). \(T\)-duality is a relation between two string theories on the level of quantum field theories. The authors of the present paper are interested in giving a precise mathematical characterization of \(T\)-duality for topological spaces. They define for any Hausdorff and paracompact topological space \(B\) a pair, \((F,h)\), over \(B\) as a principal \(T^n\)-bundle \(F\to B\), where \(T^n=U(1)\times\cdots_n\cdots U(1)\) is the \(n\)-dimensional torus, and \(h\in H^3(F;{\mathbb Z})\) such that it represents a cohomology class of twists over \(F\), by means of the isomorphism \(\left\{\text{ category of twists over }F\) Reviewer: Agostino Prástaro (Roma) Cited in 2 ReviewsCited in 18 Documents MSC: 55R15 Classification of fiber spaces or bundles in algebraic topology 55T10 Serre spectral sequences 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory Keywords:Classification of principal fiber bundles; string theory PDFBibTeX XMLCite \textit{U. Bunke} et al., Rev. Math. Phys. 18, No. 10, 1103--1154 (2006; Zbl 1116.55007) Full Text: DOI arXiv References: [1] DOI: 10.1103/PhysRevLett.92.181601 · Zbl 1267.81264 · doi:10.1103/PhysRevLett.92.181601 [2] DOI: 10.1007/s00220-004-1115-6 · Zbl 1062.81119 · doi:10.1007/s00220-004-1115-6 [3] Bouwknegt P., J. High Energy Phys. 3 pp 018– [4] DOI: 10.4310/ATMP.2005.v9.n5.a4 · Zbl 1129.53013 · doi:10.4310/ATMP.2005.v9.n5.a4 [5] DOI: 10.1007/s00220-005-1501-8 · Zbl 1115.46063 · doi:10.1007/s00220-005-1501-8 [6] DOI: 10.1142/S0129055X05002315 · Zbl 1148.55009 · doi:10.1142/S0129055X05002315 [7] DOI: 10.1142/9789812773609_0018 · doi:10.1142/9789812773609_0018 [8] DOI: 10.1016/0370-2693(87)90769-6 · doi:10.1016/0370-2693(87)90769-6 [9] DOI: 10.1016/0370-2693(88)90602-8 · doi:10.1016/0370-2693(88)90602-8 [10] DOI: 10.1007/978-1-4757-2261-1 · doi:10.1007/978-1-4757-2261-1 [11] DOI: 10.1007/s00220-004-1159-7 · Zbl 1078.58006 · doi:10.1007/s00220-004-1159-7 [12] DOI: 10.4310/ATMP.2006.v10.n1.a5 · Zbl 1111.81131 · doi:10.4310/ATMP.2006.v10.n1.a5 [13] Mukai S., Nagoya Math. J. 81 pp 153– · Zbl 0417.14036 · doi:10.1017/S002776300001922X [14] Polchinski J., Cambridge Monographs on Mathematical Physics, in: String Theory, Vols. I, II (2005) [15] DOI: 10.1016/0550-3213(96)00434-8 · Zbl 0896.14024 · doi:10.1016/0550-3213(96)00434-8 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.