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arXiv · 2603.29425

Poincar\'e duality spaces related to the Joker

Andrew Baker
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Abstract

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 Poincar\'e 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.

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Andrew Baker. 2026-03-31. Poincar\'e duality spaces related to the Joker. https://arxiv.org/abs/2603.29425

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