The signature of an even symmetric form with vanishing associated linking form

Details The signature of an even symmetric form with vanishing associated linking form The signature of an even symmetric form with vanishing associated linking form

2012-04-23

arxiv.org/abs/1204.4965v2

Mathematics

Geometric Topology

14 pages, 1 figure

Scientific paper

We prove that the signature of an even, symmetric form on a finite rank integral lattice, has signature divisible by 8, provided its associated linking form vanishes in the Witt group of linking forms. Our result generalizes the well know fact that an even, unimodular form has signature divisible by 8. We give applications to signatures of 4n-dimensional manifolds, signatures of classical knots, and provide new restrictions to solutions of certain Diophantine equations.

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