Link Invariants for Flows in Higher Dimensions
arXiv:0908.3218 · doi:10.1063/1.3427319
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 -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.
arXiv comment21+1 pages, LaTeX, no figures
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