The complex K ring of the flip Stiefel manifolds
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916221208756224 |
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| author | Basu, Samik Gondhali, Shilpa Safikaa, Fathima |
| author_facet | Basu, Samik Gondhali, Shilpa Safikaa, Fathima |
| contents | The flip Stiefel manifolds (FV_{m,2s}) are defined as the quotient of the real Stiefel manifolds (V_{m,2s}) induced by the simultaneous pairwise flipping of the co-ordinates by the cyclic group of order 2. We calculate the complex (K)-ring of the flip Stiefel manifolds, $K^\ast(FV_{m,2s})$, for $s$ even. Standard techniques involve the representation theory of $Spin(m),$ and the Hodgkin spectral sequence. However, the non-trivial element inducing the action doesn't readily yield the desired homomorphisms. Hence, by performing additional analysis, we settle the question for the case of (s \equiv 0 \pmod 2.) |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15803 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The complex K ring of the flip Stiefel manifolds Basu, Samik Gondhali, Shilpa Safikaa, Fathima K-Theory and Homology 05A10, 57S25, 19L64, 55N15, 57R15 The flip Stiefel manifolds (FV_{m,2s}) are defined as the quotient of the real Stiefel manifolds (V_{m,2s}) induced by the simultaneous pairwise flipping of the co-ordinates by the cyclic group of order 2. We calculate the complex (K)-ring of the flip Stiefel manifolds, $K^\ast(FV_{m,2s})$, for $s$ even. Standard techniques involve the representation theory of $Spin(m),$ and the Hodgkin spectral sequence. However, the non-trivial element inducing the action doesn't readily yield the desired homomorphisms. Hence, by performing additional analysis, we settle the question for the case of (s \equiv 0 \pmod 2.) |
| title | The complex K ring of the flip Stiefel manifolds |
| topic | K-Theory and Homology 05A10, 57S25, 19L64, 55N15, 57R15 |
| url | https://arxiv.org/abs/2404.15803 |