  We report the structural transformation of the low-lying spectral modes,
especially the Kohn mode, from radial to circular topology as harmonic
confining potential is modified to a toroidal one, and this corresponds to a
transition from simply to multiply connected geometry. For this we employ the
Hartree-Fock-Bogoliubov theory to examine the evolution of low energy
quasiparticles. We, then, use the Hartree-Fock-Bogoliubov theory with the Popov
approximation to demonstrate the two striking features of quantum and thermal
fluctuations. At $T=0$, the non-condensate density due to interaction induced
quantum fluctuations increases with the transformation from pancake to toroidal
geometry. The other feature is, there is a marked change in the density profile
of the non-condensate density at finite temperatures with the modification of
trapping potential. In particular, the condensate and non-condensate density
distributions have overlapping maxima in the toroidal condensate, which is in
stark contrast to the case of pancake geometry. The genesis of this difference
lies in the nature of the thermal fluctuations.
