Seminarium KMMF "Teoria Dwoistości"

The mathematical tools of Loop Quantum Gravity will be presented. The main one is the space of the parallel transports. It admits a natural compact topology, measures and geometric structures. They give rise to Hilbert spaces and operators. Generalized spin-networks are used for orthogonal decompositions. Operators represent quantum geometry. The diffeomorphism invariance plays important role. There are unsolved mathematical problems.