Link Invariants for Flows in Higher Dimensions

Abstract

Linking numbers in higher dimensions and their generalization including gauge fields are studied in the context of BF theories. The linking numbers associated to $n$-manifolds with smooth flows generated by divergence-free p-vector fields, endowed with an invariant flow measure are computed in different cases. They constitute invariants of smooth dynamical systems (for non-singular flows) and generalizes previous results for the 3-dimensional case. In particular, they generalizes to higher dimensions the Arnold's asymptotic Hopf invariant for the three-dimensional case. This invariant is generalized by a twisting with a non-abelian gauge connection. The computation of the asymptotic Jones-Witten invariants for flows is naturally extended to dimension n=2p+1. Finally we give a possible interpretation and implementation of these issues in the context of string theory.

21+1 pages, LaTeX, no figures

References in corpus (3)

• G2 Hitchin functionals at one loop
• Asymptotic Vassiliev Invariants for Vector Fields
• Asymptotic link invariants for ergodic vector fields

Cited by in corpus (4)

• Higher dimensional abelian Chern-Simons theories and their link invariants
• Application of abelian holonomy formalism to the elementary theory of numbers
• Asymptotic linking of volume-preserving actions of ${\mathbb{R}}^k$
• Vassiliev Invariants for Flows Via Chern-Simons Perturbation Theory