Cohomology between functions in a dynamical system gives an easy equivalence relation “up to coboundary”. This allows the simplification of many problems in a dynamical sense, giving us some motivation for studying these objects.
We initially look at graphs where we can define a dynamical system known as a shift of finite type. From there we will argue that this discrete model is useful for studying ergodic theory, especially hyperbolic dynamics. We will move on to talk about what coboundaries are and their properties. Finally we will look at a specific property that I have been studying and discuss one of the arguments for this.
Everything should be relatively self contained!