My understanding is that the quantization of Helicity for little group of massive particles comes from the fact that rotation in space leaves the 4-momentum $P^\mu=(m,0,0,0)$ invariant; we know that $SU(2)$ double-cover the rotation group $SO(3)$ and the irreducible representation of $SU(2)$ are labelled by $j=0,1/2,1,...$. So quantization of Helicity comes from the usual quantization of the spin representations.
For massless particles we have that the group $SO(2)\cong U(1)$ leaves the 4-momentum $P^\mu=(\omega,0,0,\omega)$ invariant. In Maggiore, Weinberg and Zee books is stated that we can't get any quantization from the (Lie) algebra of $U(1)$ and quantization comes from the topology. Maggiore mention the topology of $SL(2,\Bbb C)$, Zee mention the topology of $SO(3)$. For both authors the reasoning is that in this topologies the path that correspond to a rotation of $4\pi$ can be shrunk to a point, then we have $e^{i4\pi h}=1$ which can be satisfied only if $h=0,1/2,1,...$.
I don't understand how comes that they consider the topology of $SL(2,\Bbb C)$ or $SO(3)$, since for massless particles the group we are considering is $SO(2)\cong U(1)$
