Equivariant Topological T-Duality
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909265951719424 |
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| author | Dove, Tom Schick, Thomas |
| author_facet | Dove, Tom Schick, Thomas |
| contents | Topological T-duality is a relationship between pairs (E, P ) over a fixed space X, where E over X is a principal torus bundle and P over E is a twist, such as a gerbe of principal PU(H)-bundle. This is of interest to topologists because of the T-duality transformation: a T-duality relation between pairs (E, P ) and (F, Q ) comes with an isomorphism (with degree shift) between the twisted K-theory of E and the twisted K-theory of F. We formulate topological T-duality in the equivariant setting, following the definition of Bunke, Rumpf, and Schick. We define the T-duality transformation in equivariant K-theory and show that it is an isomorphism for actions of compact Lie groups, equal to its own inverse and uniquely characterized by naturality and a normalization for trivial situations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_06064 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Equivariant Topological T-Duality Dove, Tom Schick, Thomas K-Theory and Homology High Energy Physics - Theory Mathematical Physics Geometric Topology Topological T-duality is a relationship between pairs (E, P ) over a fixed space X, where E over X is a principal torus bundle and P over E is a twist, such as a gerbe of principal PU(H)-bundle. This is of interest to topologists because of the T-duality transformation: a T-duality relation between pairs (E, P ) and (F, Q ) comes with an isomorphism (with degree shift) between the twisted K-theory of E and the twisted K-theory of F. We formulate topological T-duality in the equivariant setting, following the definition of Bunke, Rumpf, and Schick. We define the T-duality transformation in equivariant K-theory and show that it is an isomorphism for actions of compact Lie groups, equal to its own inverse and uniquely characterized by naturality and a normalization for trivial situations. |
| title | Equivariant Topological T-Duality |
| topic | K-Theory and Homology High Energy Physics - Theory Mathematical Physics Geometric Topology |
| url | https://arxiv.org/abs/2310.06064 |