  We investigate geometrically thick disks around Kerr black holes in a
swirling universe. This stationary and axisymmetric spacetime is composed of a
Kerr black hole, which is immersed in a swirling background. The swirling
background is characterized by an odd $\mathcal{Z}_2$ symmetry, where the
northern and southern hemispheres are rotating in opposite directions. The Kerr
and swirling rotations can lead to the emergence of complex spin-spin
interactions, which heavily influence the spacetime properties. In order to
study this influence, we analyze prograde as well as retrograde circular orbits
and geometrically thick disks for different spacetime solutions, which are
classified by their Kerr parameter $a$ and the swirling parameter $j$. We find
stabilizing effects on prograde circular orbits and destabilizing effects on
retrograde circular orbits, which originate from the spin-spin interaction and
depend mainly on the Kerr rotation. Furthermore, the background rotation leads
to an emergence of static orbits and the symmetry breaking regarding the
equatorial plane causes a vertical distribution of the circular orbits and
thick torus solutions. Due to the destabilizing effect of the swirling
rotation, an outer marginally stable orbit appears, which heavily downsizes the
parameter space for disk solutions. Dependent on the Keplerian specific angular
momentum distribution of the spacetime and on the disk momentum $\ell_0$,
different types of disk are possible which we classify and which differ in
terms of the complex disk dynamics that could arise due to the presence of an
inner and outer cusp or just an outer cusp.
