A characterisation of the Z^n + Zδ lattice and definite nonunimodular intersection forms

Owens, B. and Strle, S. (2012) A characterisation of the Z^n + Zδ lattice and definite nonunimodular intersection forms. American Journal of Mathematics, 134(4), pp. 891-913. (doi:10.1353/ajm.2012.0026)

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Abstract

We prove a generalisation of Elkies’ characterisation of the Z^n lattice to nonunimodular definite forms (and lattices). Combined with inequalities of Frøyshov and of Ozsv ́ath and Szab ́o, this gives a simple test of whether a rational homology three-sphere may bound a definite four-manifold. As an example we show that small positive surgeries on torus knots do not bound negative-definite four-manifolds.

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:American Journal of Mathematics
Publisher:Johns Hopkins University Press
ISSN:0002-9327

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