We study the reflection coefficient, the transmission coefficient and the greybody factors for black holes with topologically non trivial transverse sections in 4 and d-dimensions, in the limit of low energy. Considering a massive scalar field in a t
opological massless black hole background, which is non minimally coupled to the curvature and assuming the horizon geometry with a negative constant curvature. Mainly, we show that there is range of modes which contribute to the absorption cross section in the zero-frequency limit, at difference of the result existing in the literature. Where, the mode with lowest angular momentum contribute to the absorption cross section. Also we show that the condition that the sum of the reflection coefficient and the transmission coefficient is equal to one is always satisfied for these kind of black holes.
