  Multiply-connected traps for cold, neutral atoms fix vortex cores of quantum
gases. Laguerre-Gaussian laser modes are ideal for such traps due to their
phase stability. We report theoretical calculations of the Bose-Einstein
condensation transition properties and thermal characteristics of neutral atoms
trapped in multiply connected geometries formed by Laguerre-Gaussian LG{p}{l}
beams. Specifically, we consider atoms confined to the anti-node of a LG{0}{1}
laser mode detuned to the red of an atomic resonance frequency, and those
confined in the node of a blue-detuned LG{1}{1} beam. We compare the results of
using the full potential to those approximating the potential minimum with a
simple harmonic oscillator potential. We find that deviations between
calculations of the full potential and the simple harmonic oscillator can be up
to 3%-8% for trap parameters consistent with typical experiments.
