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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Closed manifolds coming from Artinian complete intersections


Authors: Stefan Papadima and Laurentiu Paunescu
Journal: Trans. Amer. Math. Soc. 359 (2007), 2777-2786
MSC (2000): Primary 57R65, 13C40; Secondary 11E81, 58K20
Published electronically: December 20, 2006
MathSciNet review: 2286055
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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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Additional Information

Stefan Papadima
Affiliation: Institute of Mathematics “Simion Stoilow", P.O. Box 1-764, RO-014700 Bucharest, Romania
Email: Stefan.Papadima@imar.ro

Laurentiu Paunescu
Affiliation: School of Mathematics and Statistics, University of Sydney, Sydney, New South Wales 2006, Australia
Email: laurent@maths.usyd.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9947-06-04077-3
PII: S 0002-9947(06)04077-3
Keywords: $\mathbb{Q}$-surgery, artinian complete intersection, quadratic form, finite map germ
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
Article copyright: © Copyright 2006 American Mathematical Society