ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

11. Mathematical Physics

1991 MS Classification: 3, 5, 18, (54, 51, 70, 82) Leng, W. S., London T. O. E. Group, and University of Cambridge, U. K. Universal Singularity Decomposition Can singularity information needs be satisfied (structure discovered, resp. preserved) and to what extent?. .. In general singularities are found decomposable, and to arbitrary degree, even given structure conditions and constraints (for example, dimension, symmetry). Intuitively one “turns around” the singularity (example: vertex (point) singularities acquire facets, while outer-dimensionality is preserved). Formally, from the category of abstract sets to topological, geometrical, finally physical constructions and applications, we use the endomorphisms. Results: (1) Decomposable singularities preserve information (up to precisely almost-any) by singularity endomorphisms encoding;

(2) Any nonlinear or nonstandard mathematical structure in any category can be precisely structured (examples: nonstandard arithmetic, analysis, etc; nonlinear analysis, physics; non-Pythagorean geometries);

(3) the physical realisation is interpreted as pure energy states in their carrying space(s) (realising a pre-physical model T. O. E. ); this includes precise cosmological initial (singularity) conditions.