On equivariant embeddings of G-bundles
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909882295255040 |
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| author | Bakuradze, Malkhaz Meyer, Ralf |
| author_facet | Bakuradze, Malkhaz Meyer, Ralf |
| contents | For a compact group G, we give a sufficient condition for embedding one G-equivariant vector bundle into another one and for a stable isomorphism between two such bundles to imply an isomorphism. Our criteria involve multiplicities of irreducible representations of stabiliser groups. We also apply our result to ordinary nonequivariant vector bundles over the fields of quaternions, real and complex numbers and to ``real'' and ``quaternionic'' vector bundles. Our results apply to the classification of symmetry-protected topological phases of matter, providing computable bounds on the number of energy bands required to distinguish robust from fragile topological phases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00734 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On equivariant embeddings of G-bundles Bakuradze, Malkhaz Meyer, Ralf K-Theory and Homology 19L99 (primary), 19L47, 55S35 (secondary) For a compact group G, we give a sufficient condition for embedding one G-equivariant vector bundle into another one and for a stable isomorphism between two such bundles to imply an isomorphism. Our criteria involve multiplicities of irreducible representations of stabiliser groups. We also apply our result to ordinary nonequivariant vector bundles over the fields of quaternions, real and complex numbers and to ``real'' and ``quaternionic'' vector bundles. Our results apply to the classification of symmetry-protected topological phases of matter, providing computable bounds on the number of energy bands required to distinguish robust from fragile topological phases. |
| title | On equivariant embeddings of G-bundles |
| topic | K-Theory and Homology 19L99 (primary), 19L47, 55S35 (secondary) |
| url | https://arxiv.org/abs/2511.00734 |