ETD

• \ell^{2}-Betti numbers
• Simplicial Volume

The integral foliated simplicial volume is a version of simplicial volume combining the rigidity of integral coefficients with the flexibility of measure spaces. It was introduced by Gromov to estimate the \ell^{2}-Betti numbers of a closed, connected, oriented manifold.
In this thesis we will define these notions and prove a recent result by Schmidt relating the vanishing of the integral foliated simplicial volume to the vanishing of \ell^{2}-Betti numbers.