  Space asteroseismology is revolutionizing our knowledge of the internal
structure and dynamics of stars. A breakthrough is ongoing with the recent
discoveries of signatures of strong magnetic fields in the core of red giant
stars. The key signature for such a detection is the asymmetry these fields
induce in the frequency splittings of observed dipolar mixed gravito-acoustic
modes. We investigate the ability of the observed asymmetries of the frequency
splittings of dipolar mixed modes to constrain the geometrical properties of
deep magnetic fields. We use the powerful analytical Racah-Wigner algebra used
in Quantum Mechanics to characterize the geometrical couplings of dipolar mixed
oscillation modes with various possible realistic fossil magnetic fields'
topologies and compute the induced perturbation of their frequencies. First, in
the case of an oblique magnetic dipole, we provide the exact analytical
expression of the asymmetry as a function of the angle between the rotation and
magnetic axes. Its value provides a direct measure of this angle. Second,
considering a combination of axisymmetric dipolar and quadrupolar fields, we
show how the asymmetry is blind to unravel the relative strength and sign of
each component. Finally, in the case of a given multipole, we show that a
negative asymmetry is a signature of non-axisymmetric topologies. Therefore,
asymmetries of dipolar mixed modes provide key but only partial information on
the geometrical topology of deep fossil magnetic fields. Asteroseismic
constraints should therefore be combined with spectropolarimetric observations
and numerical simulations, which aim to predict the more probable stable
large-scale geometries.
