Spin Networks and Topology

Abstract

Abstract This paper discusses Penrose spin networks in relation to physics and low dimensional topology. This paper is an introduction to the relationship between Penrose spin networks and structures in physics and low dimensional topology. The paper is organised as follows. Section 2 discusses the theme of networks and discretization. Section 3 introduces the bracket model for the Jones polynomial invariant of knots and links. In Section 4 we show how the bracket state model is a natural generalization of the original Penrose spin networks, and how this model is related to the quantum group corresponding to SL(2,C).