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

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

2003-12-12

arxiv.org/abs/math/0312266v2

Mathematics

Geometric Topology

13 pages; completely rewritten with many new examples

Scientific paper

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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