"Codes, 3-manifolds and arithmetic"
Abstract: I will start the lecture by defining codes and explaining their basic idea. Then I will explain how manifolds on which an involution with finitely many fixed points acts give a code. Applying this to 3-dimensional manifolds gives particularly interesting codes: Self dual codes. I will explain that these codes are very special since they lead to unimodular lattices. An obvious question is which self dual codes come from 3-manifolds. In joint work with Volker Puppe we give a complete answer. Finally I will define a geometric condition for 3-manifolds with such an involution which leads to so called doubly even codes.