  The search for topological superconductors is one of the most pressing and
challenging questions in condensed matter and material research. Despite some
early suggestions that doping a topological insulator might be a successful
recipe to find topological superconductors, until today there is no general
understanding of the relationship of the topology of the superconductor and the
topology of its underlying normal state system. One of the major obstacles is
the strong effect of the Fermi surface and its subsequent pairing tendencies
within the Hubbard model framework, usually preventing a detailed comparison
between different topological superconducting systems. Here we present an
analysis of doped insulators - topological and trivial - where the dominant
Fermi surface effects have been equalized. Our approach allows us to study and
compare superconducting instabilities of different normal state systems and
present rigorous results about the influence of the normal state system's
topology.
