Poincaré duality spaces related to the Joker
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915914851549184 |
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| author | Baker, Andrew |
| author_facet | Baker, Andrew |
| contents | The well known Joker $\mathcal{A}(1)$-module of Adams and Priddy is known to be realisable as the cohomology of a $1$-connected space. By attaching an extra cell we obtain an $8$-dimensional Poincaré duality space whose mod~$2$ cohomology realising is an unstable $\mathcal{A}$-algebra. We use obstruction theory to show that this admits a $PL$-structure. Although we are unable to show it is smoothable, it turns out that the cohomology can be realised as that of a homogeneous space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29425 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Poincaré duality spaces related to the Joker Baker, Andrew Algebraic Topology Geometric Topology Primary 57P10, Secondary 57R67, 55S10, 55S35 The well known Joker $\mathcal{A}(1)$-module of Adams and Priddy is known to be realisable as the cohomology of a $1$-connected space. By attaching an extra cell we obtain an $8$-dimensional Poincaré duality space whose mod~$2$ cohomology realising is an unstable $\mathcal{A}$-algebra. We use obstruction theory to show that this admits a $PL$-structure. Although we are unable to show it is smoothable, it turns out that the cohomology can be realised as that of a homogeneous space. |
| title | Poincaré duality spaces related to the Joker |
| topic | Algebraic Topology Geometric Topology Primary 57P10, Secondary 57R67, 55S10, 55S35 |
| url | https://arxiv.org/abs/2603.29425 |