Closed manifolds coming from Artinian complete intersections

Papadima, Ştefan; Păunescu, Laurenţiu

doi:10.1090/S0002-9947-06-04077-3

Closed manifolds coming from Artinian complete intersections
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by Ştefan Papadima and Laurenţiu Păunescu PDF

Trans. Amer. Math. Soc. 359 (2007), 2777-2786 Request permission

Abstract:

We reformulate the integrality property of the Poincaré inner product in the middle dimension, for an arbitrary Poincaré $\mathbb {Q}$-algebra, in classical terms (discriminant and local invariants). When the algebra is $1$-connected, we show that this property is the only obstruction to realizing it by a smooth closed manifold, in dimension $8$. We analyse the homogeneous artinian complete intersections over $\mathbb {Q}$ realized by smooth closed manifolds of dimension $8$, and their signatures.

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