LIFTING REPRESENTATIONS OF KNOT GROUPS

Given a representation of a classical knot group onto a quotient group E/A, we address the classification of lifts of that representation onto E. The classification is given first in terms of classical obstruction theory and then, in many cases, interpreted in terms of the homology of covers of the knot complement. Applications include the study of dihedral, metacyclic, and metabelian representations. Properties of the restrictions of lifts to the peripheral subgroup are also studied.