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The Euler characteristic - an invariant with many incarnations

Karina Stelter (Freiburg)

Montag, 20. Januar 2020 16:15Uhr

The Euler characteristic plays a major role as a topological invariant, for example in Euler's polyhedron theorem. It can also be understood as an analytic invariant. The Poincaré-Hopf-Index theorem builds a bridge between these two realms. Furthermore, it is a geometric invariant as in the theorem of Gauß-Bonnet.

In this talk, I will focus on homologies and explain the relation between the Euler characteristic and the so-called Betti numbers, which are the rank of the homology groups of an underlying complex. The Euler characteristic is therefore also an invariant of algebraic objects.