Signatures in algebra, topology and dynamics

Étienne Ghys (1) , Andrew Ranicki (2)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 Edin. - University of Edinburgh

As the title suggests, this paper reviews some classical and less classical properties of quadratic forms and their signatures. We tried to collect several results which are not usually presented in a unified way. Our first chapter is essentially historical and describes the development of the theory of quadratic forms during the nineteenth century and the first half of the twentieth. The following chapters discuss applications to topology, dynamics and number theory, including modern developments.

Domaines: Mathématiques [math]; Algèbre commutative [math.AC]; Topologie algébrique [math.AT]; Systèmes dynamiques [math.DS]

Étienne Ghys, Andrew Ranicki. Signatures in algebra, topology and dynamics. Ensaios Matemáticos, 2016, Six papers on signatures, braids and Seifert surfaces, 30, pp.1 - 173. ⟨ensl-01405519⟩