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)

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, Professor 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