2001/04/01 by Ioannis P. Zois, Zois, Ioannis P.
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0104004
38 pages, TeX
arxiv created 2001/04/01 · openalex publication_date 2001/04/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Foliated manifolds are particular examples of noncommutative spaces. In this article 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 relating these three notions in the case of codim-1 foliations. Moreover we shall investigate its possible relation with the black hole entropy adopting the superstring theory origin of the black hole entropy in the extremal case. This situation we believe has some striking similarities with the explanation due to Bellissard of the integrality of the Hall conductivity in the quantum Hall effect. Our starting point is the Connes-Douglas-Schwarz article on compactifications of matrix models to noncommutative tori.