# 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} }

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…

## 3 Citations

### Black hole entropy, topological entropy and the Baum-Connes conjecture in K-theory

- Mathematics
- 2001

We shall try to show a relation between black hole (BH) entropy and topological entropy using the famous Baum-Connes conjecture for foliated manifolds which are particular examples of noncommutative…

### Noncommutativity vs gauge symmetry

- Mathematics
- 2003

In many aspects the most complicated noncommutative spaces correspond to foliated manifolds with nonvanishing Godbillon-Vey class. We argue that gauge invariance probably prevents a foliated manifold…

### Foliations with nonvanishing GV-class and gauge invariance

- Mathematics
- 2003

In many aspects the most complicated foliated manifolds are those with nonvanishing Godbillon-Vey class. We argue that they probably do not appear in physics and that is due to gauge symmetry which…

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