Contents

We define the Teichmüller space using the character variety . We find some kind of representations and define fuchsian representation.

We give a definition for a Hitchin representation. Using loxodromic elements we define the relative Hitchin Component.

Hitchin, Labourie, Goldman give some theorems on the Hitchin components. Interesting is, that the mapping class group acts on those components.

We do some kind of flows. This uses Goldman Flows (a generalisation of Hitchin(?) flows). The Goldman Flows are Hamiltonian flows. There are specific Flows which are called bulging flows.

Next we use Wandering sets. There is also some connection to Dehn Twist.