• Corpus ID: 14007705

Black Hole Entropy, Topological Entropy and Noncommutative Geometry

@article{Zois2001BlackHE,
title={Black Hole Entropy, Topological Entropy and Noncommutative Geometry},
author={Ioannis P. Zois},
journal={arXiv: High Energy Physics - Theory},
year={2001}
}
• I. P. Zois
• Published 1 April 2001
• Mathematics
• arXiv: High Energy Physics - Theory
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…
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References

SHOWING 1-10 OF 25 REFERENCES

String theory and noncommutative geometry

• Mathematics, Physics
• 1999
We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally

The Godbillon-Vey class, invariants of manifolds and linearised M-Theory

We apply the Godbillon-Vey class to compute the transition amplitudes between some non-commutative solitons in M-Theory; our context is that of Connes-Douglas-Schwarz where they considered

The origin of black hole entropy

In this thesis properties and the origin of black hole entropy are investigated from various points of view. First, laws of black hole thermodynamics are reviewed. In particular, the first and

Noncommutative Geometry and Matrix Theory: Compactification on Tori

• Mathematics
• 1997
We study toroidal compactification of Matrix theory, using ideas and results of noncommutative geometry. We generalize this to compactification on the noncommutative torus, explain the classification

The Origin of Black Hole Entropy in String Theory

I review some recent work in which the quantum states of string theory which are associated with certain black holes have been identified and counted. For large black holes, the number of states

A New Invariant for σ Models

Abstract: We introduce a \emph{new} invariant for $\sigma$ models (and foliations more generally) using the \emph{even} pairing between K-homology and cyclic homology. We try to calculate it for the

The graph of a foliation

AbstractLet M be a riemannian manifold with a riemannian foliation F. Among other things we construct a special metric on the graph of the foliation, $$\mathfrak{G}(F)$$ , (which is complete, when M

Some remarks on foliations with minimal leaves

Let ^ be a foliation on a manifold X of dimension n = p + q, the leaves being submanifolds of dimension p and codimension q. Everything will be assumed to be of class C 0 0 . The question of the

Introduction to Ergodic Theory

Ergodic theory concerns with the study of the long-time behavior of a dynamical system. An interesting result known as Birkhoff’s ergodic theorem states that under certain conditions, the time