Yet another Hopf Invariant
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2015
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| _version_ | 1866909537813921792 |
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| author | Doeraene, Jean-Paul Haouari, Mohammed El |
| author_facet | Doeraene, Jean-Paul Haouari, Mohammed El |
| contents | The classical Hopf invariant is defined for a map f: S^r -> X. Here we define `hcat' which is some kind of Hopf invariant built with a construction in Ganea's style, valid for maps not only on spheres but more generally on a `relative suspension' f: Sigma_A W -> X. We study the relation between this invariant and the sectional category and the relative category of a map. In particular, for f being the `restriction' of f on A, we have relcat(i) <= hcat(f) <= relcat(i) + 1 and relcat(f) <= hcat(f). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1501_03712 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Yet another Hopf Invariant Doeraene, Jean-Paul Haouari, Mohammed El Algebraic Topology 55Q25, 55M30 The classical Hopf invariant is defined for a map f: S^r -> X. Here we define `hcat' which is some kind of Hopf invariant built with a construction in Ganea's style, valid for maps not only on spheres but more generally on a `relative suspension' f: Sigma_A W -> X. We study the relation between this invariant and the sectional category and the relative category of a map. In particular, for f being the `restriction' of f on A, we have relcat(i) <= hcat(f) <= relcat(i) + 1 and relcat(f) <= hcat(f). |
| title | Yet another Hopf Invariant |
| topic | Algebraic Topology 55Q25, 55M30 |
| url | https://arxiv.org/abs/1501.03712 |