2000/11/25 by Ioannis P. Zois, Zois, Ioannis P.
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0011228
39 pages, TeX
arxiv created 2000/11/25 · openalex publication_date 2000/11/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We try to give a qualitative description of the Godbillon-Vey class and its relation on the one hand to the holonomy and on the other hand to the topological entropy of a foliation, using a remarkable theorem proved recently by G. Duminy (which still remains unpublished), relating these three notions in the case of codim-1 foliations. Moreover we shall investigate its possible consequences on string theory. In particular we shall present a conceptual argument according to which the curvature of the B-field (rank two antisymmetric tensor) of open strings might be related to the Godbillon-Vey class using a suitable generalisation of ``Non-Abelian Geometry'' which has just appeared in physics literature. Our starting point again is the Connes-Douglas-Schwarz article on compactifications of matrix models to noncommutative tori.