### 3-Sphären mit kleinen Eckenvalenzen.

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An approach to construction of topological invariants of the Reshetikhin-Turaev-Witten type of 3- and 4-dimensional manifolds in the framework of SU(2) Chern-Simons gauge theory and its hidden (quantum) gauge symmetry is presented.

We give a self-contained introduction to the theory of shadows as a tool to study smooth 3-manifolds and 4-manifolds. The goal of the present paper is twofold: on the one hand, it is intended to be a shortcut to a basic use of the theory of shadows, on the other hand it gives a sketchy overview of some of the most recent results on shadows. No original result is proved here and most of the details of the proofs are left out.