  Topological stars, or top stars for brevity, are smooth horizonless static
solutions of Einstein-Maxwell theory in 5-d that reduce to spherically
symmetric solutions of Einstein-Maxwell-Dilaton theory in 4-d. We study linear
scalar perturbations of top stars and argue for their stability and
deformability. We tackle the problem with different techniques including WKB
approximation, numerical analysis, Breit-Wigner resonance method and quantum
Seiberg-Witten curves. We identify three classes of quasi-normal modes
corresponding to prompt-ring down modes, long-lived meta-stable modes and what
we dub `blind' modes. All mode frequencies we find have negative imaginary
parts, thus suggesting linear stability of top stars. Moreover we determine the
tidal Love and dissipation numbers encoding the response to tidal deformations
and, similarly to black holes, we find zero value in the static limit but,
contrary to black holes, we find non-trivial dynamical Love numbers and
vanishing dissipative effects at linear order. For the sake of illustration in
a simpler context, we also consider a toy model with a piece-wise constant
potential and a centrifugal barrier that captures most of the above features in
a qualitative fashion.
