Studying and removing effects of fixed topology

At small lattice spacing, or when using overlap fermions, lattice QCD simulations tend to become stuck in a single topological sector. Physical observables, e.g.\ hadron masses, then differ from their full QCD counterparts by $1\mathrm{/}V$ corrections, where $V$ is the spacetime volume. These corrections can be calculated order by order using the saddle point method. We calculate all corrections proportional to $1\mathrm{/}{V}^2$ and $1\mathrm{/}{V}^3$ and test the resulting equations for several models: a quantum mechanical particle on a circle, the Schwinger model and SU(2) Yang-Mills theory.