Abstract

We prove a generalization of Elkies' characterization of the ${\Bbb{Z}}^n$ lattice to nonunimodular definite forms (and lattices). Combined with inequalities of Fr{\o}yshov and of Ozsv\'{a}th 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.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 891-913
Launched on MUSE
2012-07-25
Open Access
No
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