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

2008/02/11 by Brendan Owens, Owens, Brendan, Saso Strle +1
Mathematics · #11H55 #57M27 #57Q60 #57R58. #FOS: Mathematics #Geometric Topology (math.GT) #Number Theory (math.NT) #math.GT #math.NT #msc:11H55 #msc:57M27 #msc:57Q60 #msc:57R58.

paper · pdf · doi:10.48550/arxiv.0802.1495

21 pages, 1 figure

arxiv created 2008/02/11 · arxiv updated 2009/12/01

Abstract

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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