
TL;DR
This paper constructs an 8-dimensional Poincaré duality space with a specific cohomology algebra related to the Joker module, and proves it admits a PL-structure using obstruction theory.
Contribution
It introduces a new Poincaré duality space with a cohomology algebra linked to the Joker module and establishes its PL-structure.
Findings
The space's cohomology is realizable as an unstable algebra.
The space admits a PL-structure.
Cohomology can be realized as that of a homogeneous space.
Abstract
The well known Joker -module of Adams and Priddy is known to be realisable as the cohomology of a -connected space. By attaching an extra cell we obtain an -dimensional Poincar\'e duality space whose mod~ cohomology realising is an unstable -algebra. We use obstruction theory to show that this admits a -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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