  We investigate both the hyperbolic action and the determinant ratio action
designed to fix the topological charge on the lattice. We show to what extent
topology is fixed depending on the parameters of these actions, keeping the
physical situation fixed. At the same time the agreement between different
definitions of topological charge - the field theoretic and the index
definition - is directly correlated to the degree topology is fixed. Moreover,
it turns out that the two definitions agree very well. We also study finite
volume effects arising in the static potential and related quantities due to
topology fixing.
