Formes de Seifert et formes quadratiques entières. (Seifert forms and integral quadratic forms) (Q1073827)

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.