  Stellar oscillations can be of topological origin. We reveal this deep and
so-far hidden property of stars by establishing a novel parallel between stars
and topological insulators. We construct an hermitian problem to derive the
expression of the stellar $\mathrm{\textit{acoustic-buoyant}}$ frequency $S$ of
non-radial adiabatic pulsations. A topological analysis then connects the
changes of sign of the acoustic-buoyant frequency to the existence of Lamb-like
waves within the star. These topological modes cross the frequency gap and
behave as gravity modes at low harmonic degree $\ell$ and as pressure modes at
high $\ell$. $S$ is found to change sign at least once in the bulk of most
stellar objects, making topological modes ubiquitous across the
Hertzsprung-Russel diagram. Some topological modes are also expected to be
trapped in regions where the internal structure varies strongly locally.
