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Loop quantum gravity is a physical theory which aims at unifying generalrelativity and quantum mechanics. It takes general relativity very seriouslyand modifies it via a quantisation. General relativity describes gravity interms of geometry. Therefore, quantising such theory must be equivalent toquantising geometry and that is what loop quantum gravity does. This soundslike a mathematical task as well. This is why in this paper we will present themathematics of loop quantum gravity. We will do it from a mathematician pointof view. This paper is intended to be an introduction to loop quantum gravityfor postgraduate students of physics and mathematics. In this work we willrestrict ourselves to the three dimensional case.

Quantum Geometry II : The Mathematics of Loop Quantum Gravity Three dimensional quantum gravity