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

2003/12/12 by Brendan Owens, Owens, Brendan, Sašo Strle +2
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.GT #math.NT

paper · pdf · doi:10.48550/arxiv.math/0312266

13 pages; completely rewritten with many new examples

openalex publication_date 2003/12/12 · arxiv created 2004/04/15 · arxiv updated 2009/12/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

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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