A characterisation of the n<1>+<3> form and applications to rational homology spheres

Owens, B. and Strle, S. (2006) A characterisation of the n<1>+<3> form and applications to rational homology spheres. Mathematical Research Letters, 13(2), pp. 259-271.

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Publisher's URL: http://www.mrlonline.org/mrl/2006-013-002/2006-013-002-007.html

Abstract

We conjecture two generalisations of Elkies' theorem on unimodular quadratic forms to non-unimodular forms. We give some evidence for these conjectures including a result for determinant 3. These conjectures, when combined with results of Froyshov and of Ozsvath and Szabo, would give a simple test of whether a rational homology 3-sphere may bound a negative-definite four-manifold. We verify some predictions using Donaldson's theorem. Based on this we compute the four-ball genus of some Montesinos knots.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Owens, Dr Brendan
Authors: Owens, B., and Strle, S.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Mathematical Research Letters
ISSN:1073-2780
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