Geometric construction of classes in van Daele's K-theory
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912088489721856 |
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| author | Joseph, Collin Mark Meyer, Ralf |
| author_facet | Joseph, Collin Mark Meyer, Ralf |
| contents | We describe explicit generators for the "real" K-theory of "real" spheres in van Daele's picture. Pulling these generators back along suitable maps from tori to spheres produces a family of Hamiltonians used in the physics literature on topological insulators. We compute their K-theory classes geometrically, based on wrong-way functoriality of K-theory and the geometric version of bivariant K-theory, which we extend to the "real" case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_16245 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Geometric construction of classes in van Daele's K-theory Joseph, Collin Mark Meyer, Ralf K-Theory and Homology We describe explicit generators for the "real" K-theory of "real" spheres in van Daele's picture. Pulling these generators back along suitable maps from tori to spheres produces a family of Hamiltonians used in the physics literature on topological insulators. We compute their K-theory classes geometrically, based on wrong-way functoriality of K-theory and the geometric version of bivariant K-theory, which we extend to the "real" case. |
| title | Geometric construction of classes in van Daele's K-theory |
| topic | K-Theory and Homology |
| url | https://arxiv.org/abs/2211.16245 |