  We study a spin-polarized degenerate Fermi gas interacting via a p-wave
Feshbach resonance in an optical lattice. The strong confinement available in
this system allows us to realize one- and two-dimensional gases and therefore
to restrict the asymptotic scattering states of atomic collisions. When
aligning the atomic spins along (or perpendicular to) the axis of motion in a
one-dimensional gas, scattering into channels with the projection of the
angular momentum of |m|=1 (or m=0) can be inhibited. In two and three
dimensions we observe the doublet structure of the p-wave Feshbach resonance.
Both for the one-dimensional and the two-dimensional gas we find a shift of the
position of the resonance with increasing confinement due to the change in
collisional energy. In a three-dimensional optical lattice the losses on the
Feshbach resonance are completely suppressed.
