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.References
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Additional Information
- Ştefan Papadima
- Affiliation: Institute of Mathematics “Simion Stoilow", P.O. Box 1-764, RO-014700 Bucharest, Romania
- Email: Stefan.Papadima@imar.ro
- Laurenţiu Păunescu
- Affiliation: School of Mathematics and Statistics, University of Sydney, Sydney, New South Wales 2006, Australia
- Email: laurent@maths.usyd.edu.au
- Received by editor(s): July 26, 2004
- Received by editor(s) in revised form: April 12, 2005
- Published electronically: December 20, 2006
- Additional Notes: The authors were partially supported by grant U4249 Sesqui R&D/2003 of the University of Sydney
- © Copyright 2006 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 359 (2007), 2777-2786
- MSC (2000): Primary 57R65, 13C40; Secondary 11E81, 58K20
- DOI: https://doi.org/10.1090/S0002-9947-06-04077-3
- MathSciNet review: 2286055