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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 57R65, 13C40, 11E81, 58K20

Retrieve articles in all journals with MSC (2000): 57R65, 13C40, 11E81, 58K20

Additional Information

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

Laurentiu Paunescu
Affiliation: School of Mathematics and Statistics, University of Sydney, Sydney, New South Wales 2006, Australia

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