RELATIONAL TOPOLOGY AS THE FOUNDATION FOR QUANTUM GRAVITY.

We propose a new approach to the quantum theory of gravitation, in which the point sets of regions of spacetime are replaced by objects in a category. The objects can be constructed as limits of spin foam models, thus directly connecting to approximations to general relativity which have already been studied, and leading to a mathematically natural interpretation of the meaning of the triangulations in the spin foam models. The physical motivation for our proposal is a connection between ideas about the limited amount of information which can flow from one region to another in General Relativity, an analysis of the problem of the infinities in QFT, and the relational or categorical approach to topology in abstract homotopy theory and algebraic geometry. [ABSTRACT FROM AUTHOR]