A Characterisation of the Z ⊕ 3z Lattice and Applications to Rational Homology Spheres
نویسنده
چکیده
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 Frøyshov and of Ozsváth and Szabó, 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.
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