  We study the ground state of spinless fermions living on a sphere across
$p$-wave Feschbach resonances. By construsting a microscopic model of fermions
on a general curved surface, we show that the Guassian curvature induces an
emergent magnetic field coupled to the $p\pm ip$ order parameters. In the case
of a sphere, the magnetic field corresponds to a Dirac monopole field, which
causes topological defects in the superfluid ground state. Using the BCS mean
field theory, we calculate its many-body ground state self consistently and
give the phase diagram. The ground state may exhibit two types of topological
defects, two voritces on the south and north pole or a domain wall which
separates $p_\theta+ ip_\phi$ and $p_\theta-ip_\phi$ superfluids.
