Orientable manifolds with nonzero dual Stiefel-Whitney classes of largest possible grading
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909713721982976 |
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| author | Davis, Donald M. |
| author_facet | Davis, Donald M. |
| contents | It is known that, for all n, there exist compact differentiable orientable n-manifolds with dual Stiefel-Whitney class wbar_{n-ahat(n)} nonzero, and this is best possible, but the proof is nonconstructive. Here ahat(n) equals the number of 1's in the binary expansion of n if n equiv 1 mod 4 and exceeds this by 1 otherwise. We find, for all n nonzero mod 4, examples of real Bott manifolds with this property. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_23482 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orientable manifolds with nonzero dual Stiefel-Whitney classes of largest possible grading Davis, Donald M. Algebraic Topology Geometric Topology 57R20, 57R19, 55S10 It is known that, for all n, there exist compact differentiable orientable n-manifolds with dual Stiefel-Whitney class wbar_{n-ahat(n)} nonzero, and this is best possible, but the proof is nonconstructive. Here ahat(n) equals the number of 1's in the binary expansion of n if n equiv 1 mod 4 and exceeds this by 1 otherwise. We find, for all n nonzero mod 4, examples of real Bott manifolds with this property. |
| title | Orientable manifolds with nonzero dual Stiefel-Whitney classes of largest possible grading |
| topic | Algebraic Topology Geometric Topology 57R20, 57R19, 55S10 |
| url | https://arxiv.org/abs/2507.23482 |