On the intersection form of surfaces

Daniel Massart (1) , Bjoern Muetzel (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

Given a closed, oriented surface M, the algebraic intersection of closed curves induces a symplectic form Int(.,.) on the first homology group of M. If M is equipped with a Riemannian metric g, the first homology group of M inherits a norm, called the stable norm. We study the norm of the bilinear form Int(.,.), with respect to the stable norm.

Mots clés: homology; intersection form; surfaces

Domaines: Géométrie différentielle [math.DG]; Systèmes dynamiques [math.DS]

Daniel Massart, Bjoern Muetzel. On the intersection form of surfaces. Manuscripta mathematica, 2014, 143 (1), pp.19-49. ⟨10.1007/s00229-013-0615-0⟩. ⟨hal-00800540⟩