A Study of topology of the Flip Stiefel Manifolds
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929325844987904 |
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| author | Basu, Samik Fathima, Safikaa Gondhali, Shilpa |
| author_facet | Basu, Samik Fathima, Safikaa Gondhali, Shilpa |
| contents | A well known quotient of the real Stiefel manifold is the projective Stiefel manifold. We introduce a new family of quotients of the real Stiefel manifold by cyclic group of order 2 whose action is induced by simultaneous pairwise flipping of the coordinates. We obtain a description for their tangent bundles, compute their mod 2 cohomology and compute Stiefel Whitney classes of these manifolds. We use these to give applications to their stable span, parallelizability and equivariant maps, and the associated results in topological combinatorics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_12702 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Study of topology of the Flip Stiefel Manifolds Basu, Samik Fathima, Safikaa Gondhali, Shilpa Algebraic Topology Primary : 57T15, 57S17 Secondary : 57R20, 55T10 A well known quotient of the real Stiefel manifold is the projective Stiefel manifold. We introduce a new family of quotients of the real Stiefel manifold by cyclic group of order 2 whose action is induced by simultaneous pairwise flipping of the coordinates. We obtain a description for their tangent bundles, compute their mod 2 cohomology and compute Stiefel Whitney classes of these manifolds. We use these to give applications to their stable span, parallelizability and equivariant maps, and the associated results in topological combinatorics. |
| title | A Study of topology of the Flip Stiefel Manifolds |
| topic | Algebraic Topology Primary : 57T15, 57S17 Secondary : 57R20, 55T10 |
| url | https://arxiv.org/abs/2308.12702 |