  In this paper we further explore the question of topological charge in the
center vortex-nexus picture of gauge theories. Generally, this charge is
locally fractionalized in units of 1/N for gauge group SU(N), but globally
quantized in integral units. We show explicitly that in d=4 global topological
charge is a linkage number of the closed two-surface of a center vortex with a
nexus world line, and relate this linkage to the Hopf fibration, with homotopy
$\Pi_3(S^3)\simeq Z$; this homotopy insures integrality of the global
topological charge. We show that a standard nexus form used earlier, when
linked to a center vortex, gives rise naturally to a homotopy $\Pi_2(S^2)\simeq
Z$, a homotopy usually associated with 't Hooft-Polyakov monopoles and similar
objects which exist by virtue of the presence of an adjoint scalar field which
gives rise to spontaneous symmetry breaking. We show that certain integrals
related to monopole or topological charge in gauge theories with adjoint
scalars also appear in the center vortex-nexus picture, but with a different
physical interpretation. We find a new type of nexus which can carry
topological charge by linking to vortices or carry d=3 Chern-Simons number
without center vortices present; the Chern-Simons number is connected with
twisting and writhing of field lines, as the author had suggested earlier. In
general, no topological charge in d=4 arises from these specific static
configurations, since the charge is the difference of two (equal) Chern-Simons
number, but it can arise through dynamic reconnection processes. We complete
earlier vortex-nexus work to show explicitly how to express globally-integral
topological charge as composed of essentially independent units of charge 1/N.
