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Spectral flow for flux tube systems and K-theory Getz, Alan
Abstract
We study families of Hamiltonians on the lattice arising from the insertion of N flux tubes through lattice cells. In particular, it is shown such systems, under an appropriate notion of equivalence, are in bijective correspondence with the first K-group of the N-torus. A version of spectral flow is defined in the context of systems arising from flux tubes, which serves as an invariant of these systems, and it is shown that this provides a classification for N = 1, 2, and fails to do so for N ≥ 3. We also show that for any path connected locally compact Hausdorff space X, spectral flow can be used to generate a natural homomorphism from the first K-group of X to the first cohomology group of X. Finally, we show that if X is a connected finite CW complex with abelain fundamental group, then this map is surjective.
Item Metadata
| Title |
Spectral flow for flux tube systems and K-theory
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| Creator | |
| Supervisor | |
| Publisher |
University of British Columbia
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| Date Issued |
2023
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| Description |
We study families of Hamiltonians on the lattice arising from the insertion of N flux tubes through lattice cells. In particular, it is shown such systems, under an appropriate notion of equivalence, are in bijective correspondence with the first K-group of the N-torus. A version of spectral flow is defined in
the context of systems arising from flux tubes, which serves as an invariant of these systems, and it is shown that this provides a classification for N = 1, 2, and fails to do so for N ≥ 3. We also show that for any path connected locally compact Hausdorff space X, spectral flow can be used to generate a
natural homomorphism from the first K-group of X to the first cohomology group of X. Finally, we show that if X is a connected finite CW complex with abelain fundamental group, then this map is surjective.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2023-08-22
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0435531
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2023-11
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| Campus | |
| Scholarly Level |
Graduate
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International