Kan man ved den Baudouinske Reaktion paa Sesamolje forveksle Natursmør med Margarine.

Kan man ved den Baudouinske Reaktion paa Sesamolje forveksle Natursmør med Margarine

Black Hole Entropy, Topological Entropy and the Baum-Connes Conjecture in K-Theory

We shall try to exhibit a relation between black hole entropy and topological entropy using the famous Baum-Connes conjecture for foliated manifolds which are particular examples of noncommutative spaces. Our argument is qualitative and it is based on the microscopic origin of the Beckenstein-Hawking area-entropy formula for black holes, provided by superstring theory, in the more general noncommutative geometric context of M-Theory following the Connes- Douglas-Schwarz article.Comment: 17 pages, Latex, contains an important paragraph in section 2 which gives a better understandin

Operators, Algebras and their Invariants for Aperiodic Tilings

We review the construction of operators and algebras from tilings of Euclidean space. This is mainly motivated by physical questions, in particular after topological properties of materials. We explain how the physical notion of locality of interaction is related to the mathematical notion of pattern equivariance for tilings and how this leads naturally to the definition of tiling algebras. We give a brief introduction to the K-theory of tiling algebras and explain how the algebraic topology of K-theory gives rise to a correspondence between the topological invariants of the bulk and its boundary of a material. 1.1 Tilings and the topology of their hulls In condensed matter theory tilings are used to describe the spatial arrangement of the constitutents which make up a material, for instance a quasicrys-tal. They describe the spatial structure of the material. Associated to a tiling are various topological spaces and topological dy-namical systems. Their topology is peculiar. It takes into account the topology of the space in which the tiling lies and, at the same time, its pattern structure , that is, the way how finite patterns repeat over the tiling. Continuity in the tiling topology is related to locality in physics