Formes de Seifert et formes quadratiques entières. (Seifert forms and integral quadratic forms)
type: Item
instance of: scholarly article
title: Formes de Seifert et formes quadratiques entières. (Seifert forms and integral quadratic forms)
zbMATH Open document ID: 0589.10023
published in: L'Enseignement Mathématique. 2e Série
publication date: 1985-01-01T00:00:00Z
review text: Let S be a unimodular \(\epsilon\)-symmetric \((\epsilon =\pm 1)\) bilinear form on a finitely generated free \({\mathbb{Z}}\)-module L. Motivated by problems in knot theory the author studies the following question: Is there a (not necessarily symmetric) bilinear form A on L such that \(S=A+\epsilon A'\) \((A'=transposed\) of A). For \(\epsilon =-1\) or \(\epsilon =1\) and S indefinite a complete answer is given. For \(\epsilon =1\) and S definite the problem is related to the existence of isometries \(t: X\to X\), such that 1-t is an isomorphism, on certain indecomposable sublattices X of L. In particular this leads to a complete answer in the low dimensions 8, 16 and 24.
Mathematics Subject Classification ID: 11E16
Mathematics Subject Classification ID: 57Q45
zbMATH DE Number: 3946225
zbMATH Keywords: Seifert form
zbMATH Keywords: indecomposable lattice
zbMATH Keywords: bilinear form
zbMATH Keywords: knot theory
zbMATH Keywords: existence of isometries
author: Michel Kervaire
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3946225