  We show that the rotating Rayleigh-Benard convection, where a rotating fluid
is heated from below, exhibits non-Hermitian topological states. Recently,
Favier and Knobloch (JFM 2020) hypothesized that the robust wall modes in
rapidly rotating convection are topologically protected. We study the linear
problem around the conduction profile, and by considering a Berry curvature
defined in the complex wavenumber space, particularly, by introducing a complex
vertical wavenumber, we find that these modes can be characterized by a
non-zero integer Chern number, indicating their topological nature. The
eigenvalue problem is intrinsically non-Hermitian, therefore the definition of
Berry curvature generalizes that of the stably stratified problem. Moreover,
the three-dimensional setup naturally regularizes the eigenvector at the
infinite horizontal wavenumber. Under the hydrostatic approximation, it
recovers a two-dimensional analogue of the one which explains the topological
origin of the equatorial Kelvin and Yanai waves. The existence of the tenacious
wall modes relies only on rotation when the fluid is stratified, no matter
whether it is stable or unstable. However, the neutrally stratified system does
not support a topological edge state. In addition, we define a winding number
to visualize the topological nature of the fluid.
