  Because the magneto-rotational instability is capable of exponentially
amplifying weak preexisting magnetic fields, it might be hoped that the
character of the magnetic field in accretion disks is independent of the nature
of the seed field. However, the divergence-free nature of magnetic fields in
highly conducting fluids ensures that their large-scale topology is preserved,
no matter how greatly the field intensity is changed. By performing global
two-dimensional and three-dimensional general relativistic magnetohydrodynamic
disk simulations with several different topologies for the initial magnetic
field, we explore the degree to which the character of the flows around black
holes depends on the initial topology. We find that while the qualitative
properties of the accretion flow are nearly independent of field topology,
jet-launching is very sensitive to it: a sense of vertical field consistent for
at least an inner disk inflow time is essential to the support of strong jets.
