A Dehn surgery description of regular finite cyclic covering spaces of rational homology spheres

Abstract

We provide related Dehn surgery descriptions for rational homology spheres and a class of their regular finite cyclic covering spaces. As an application, we use the surgery descriptions to relate the Casson invariants of the covering spaces to that of the base space. Finally, we show that this places restrictions on the number of finite and cyclic Dehn fillings of the knot complements in the covering spaces beyond those imposed by Culler-Gordon-Luecke-Shalen and Boyer-Zhang.