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

2012/04/23 by Stanislav Jabuka, Jabuka, Stanislav
Mathematics · #57M99 #57N99 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1204.4965

openalex publication_date 2012/04/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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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