The topology of events

Abstract

A matrix model is constructed to compute characteristic numbers of the space of subsets of $R^d $ with $N$ elements. This matrix model is found to be a constrained null dimensional reduction to a point of a Yang-Mills theory with anticommuting matter in $d+2$ dimensions. The constraints and equations of motion are similar to those found by Nishino and Sezgin in their 10+2 dimensional supersymmetric Yang-Mills equations. It is conjectured that the $d=10$ topological model is a twisted form of the Nishino-Sezgin model, dimensionally reduced to a point, due to SO(8) triality. Topological matrix models are constructed for non-commutative spaces, entirely in terms of algebras associated with such spaces. These models exhibit degrees of freedom analogous to massive modes in string theory.