On Braid Excitations in Quantum Gravity

We propose a new notation for the states in some models of quantum gravity, namely 4-valent spin networks embedded in a topological three manifold. With the help of this notation, equivalence moves, namely translations and rotations, can be defined, which relate the projections of diffeomorphic embeddings of a spin network. Certain types of topological structures, viz 3-strand braids as local excitations of embedded spin networks, are defined and classified by means of the equivalence moves. This paper formulates a mathematical approach to the further research of particle-like excitations in quantum gravity.