Geodesic
On finite domination and Poincaré duality
Homology, homotopy, and applications, Tome 26 (2024) no. 1, pp. 29-35.

Voir la notice de l'article provenant de la source International Press of Boston

The object of this paper is to show that non-homotopy finite Poincaré duality spaces are plentiful. Let $π$ be a finitely presented group. Assuming that the reduced Grothendieck group $\widetilde{K}_0 (\mathbb{Z} [\pi])$ has a non-trivial $2$-divisible element, we construct a finitely dominated Poincaré space $X$ with fundamental group $π$ such that $X$ is not homotopy finite. The dimension of $X$ can be made arbitrarily large. Our proof relies on a result which says that every finitely dominated space possesses a stable Poincaré duality thickening.
DOI : 10.4310/HHA.2024.v26.n1.a3
Classification : 19J05, 57P10, 16E20
Keywords: Poincaré duality space, finite domination, Wall finiteness obstruction 
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John R. Klein. On finite domination and Poincaré duality. Homology, homotopy, and applications, Tome 26 (2024) no. 1, pp. 29-35. doi : 10.4310/HHA.2024.v26.n1.a3. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2024.v26.n1.a3/

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