Topological Geometrodynamics: an Overall View

A brief summary of the basic ideas of Topological Geometrodynamics (TGD) is given with a special emphasis on the most recent mathematical developments. There are several first principle approaches to quantum TGD. The basic dynamical objects are light-like 3-surfaces which means a generalization of the conformal symmetries of super string models and implies a parton level formulation of quantum TGD as an almost topological quantum field theory with discrete symplectic fusion algebras playing a key role in the formulation of theory. The notion of finite measurement resolution realized in terms of inclusions of hyperfinite factors of type 111 can be also taken as a fondamental dynamical principle. Associativity -in both number theoretical sense and in the sense of conformal field theories -and number theoretical universality stating that the scattering amplitudes make sense in both real and p-adic number fields define further principles of this kind. All these approaches lead to the notion of number theoretical braid meaning discretization at space-time level. The notion of operad is tailor made for formulating the notion of finite measurement resolution and rather precise formulation of generalized Feynman diagrammatics emerges in this framework.