A characterisation of the Z^n + Z(δ) lattice and definite nonunimodular intersection forms

Details A characterisation of the Z^n + Z(δ) lattice and definite nonunimodular intersection forms A characterisation of the Z^n + Z(δ) lattice and definite nonunimodular intersection forms

2008-02-11

arxiv.org/abs/0802.1495v1

Mathematics

Geometric Topology

21 pages, 1 figure

Scientific paper

We prove a generalisation of Elkies' theorem to nonunimodular definite forms
(and lattices). Combined with inequalities of Froyshov and of Ozsvath and
Szabo, this gives a simple test of whether a rational homology 3-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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