  We consider torsional oscillations that are trapped in a layer of
spherical-hole (bubble) nuclear structure, which is expected to occur in the
deepest region of the inner crust of a neutron star. Because this layer
intervenes between the phase of slab nuclei and the outer core of uniform
nuclear matter, torsional oscillations in the bubble phase can be excited
separately from usual crustal torsional oscillations. We find from eigenmode
analyses for various models of the equation of state of uniform nuclear matter
that the fundamental frequencies of such oscillations are almost independent of
the incompressibility of symmetric nuclear matter, but strongly depend on the
slope parameter of the nuclear symmetry energy $L$. Although the frequencies
are also sensitive to the entrainment effect, i.e., what portion of nucleons
outside bubbles contribute to the oscillations, by having such a portion fixed,
we can successfully fit the calculated fundamental frequencies of torsional
oscillations in the bubble phase inside a star of specific mass and radius as a
function of $L$. By comparing the resultant fitting formula to the frequencies
of quasi-periodic oscillations (QPOs) observed from the soft-gamma repeaters,
we find that each of the observed low-frequency QPOs can be identified either
as a torsional oscillation in the bubble phase or as a usual crustal
oscillation, given generally accepted values of $L$ for all the stellar models
considered here.
