  The two-dimensional Schwinger model is used to explore how lattice fermion
operators perceive the global topological charge $q \in \mathbb{Z}$ of a given
background gauge field. We focus on Karsten-Wilczek and Borici-Creutz fermions,
which are minimally doubled, and compare them to Wilson, Brillouin, naive,
staggered and Adams fermions. For each operator the eigenvalue spectrum in a
background with $q \neq 0$ is determined along with the chiralities of the
eigenmodes, and the spectral flow of the pertinent hermitean operator is worked
out. We find that Karsten-Wilczek and Borici-Creutz fermions perceive the
global topological charge $q$ in the same way as staggered and naive fermions
do.
