  We study the formation of vortices, vortex necklaces and vortex ring
structures as a result of the interference of higher-dimensional Bose-Einstein
condensates (BECs). This study is motivated by earlier theoretical results
pertaining to the formation of dark solitons by interfering quasi
one-dimensional BECs, as well as recent experiments demonstrating the formation
of vortices by interfering higher-dimensional BECs. Here, we demonstrate the
genericity of the relevant scenario, but also highlight a number of additional
possibilities emerging in higher-dimensional settings. A relevant example is,
e.g., the formation of a "cage" of vortex rings surrounding the
three-dimensional bulk of the condensed atoms. The effects of the relative
phases of the different BEC fragments and the role of damping due to coupling
with the thermal cloud are also discussed. Our predictions should be
immediately tractable in currently existing experimental BEC setups.
