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

Brendan Owens; Saso Strle

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

Brendan Owens·Saso Strle

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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.

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Brendan Owens, Saso Strle. 2004-04-15. A characterisation of the n<1> + <3> form and applications to rational homology spheres. https://arxiv.org/abs/math/0312266

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