Signatures in algebra, topology and dynamics

Abstract

We survey the 19th century development of the signature of a quadratic form, and the applications in the 20th and 21st century to the topology of manifolds and dynamical systems. Version 2 is an expanded and corrected version of Version 1, including an Appendix by the second named author "Algebraic L-theory of rings with involution and the localization exact sequence".

Published in Ensaios Matematicos "Six papers on signatures, braids and Seifert surfaces" http://ensaios.sbm.org.br/contents/