A norm for the cohomology of 2-complexes

Vladimir Turaev (1)

1 IRMA - Institut de Recherche Mathématique Avancée

We introduce a norm on the real 1-cohomology of finite 2-complexes determined by the Euler characteristics of graphs on these complexes. We also introduce twisted Alexander-Fox polynomials of groups and show that they give rise to norms on the real 1-cohomology of groups. Our main theorem states that for a finite 2-complex X, the norm on H^1(X; R) determined by graphs on X majorates the Alexander-Fox norms derived from \pi_1(X).

Domaines: Matière Molle [cond-mat.soft]

Vladimir Turaev. A norm for the cohomology of 2-complexes. Algebraic and Geometric Topology, 2002, 2, pp.137-155. ⟨10.2140/agt.2002.2.137⟩. ⟨hal-00104617⟩