In this paper we define a new invariant of the incomplete hyperbolic
structures on a 1-cusped finite volume hyperbolic 3-manifold M, called the
ortholength invariant. We show that away from a (possibly empty) subvariety of
excluded values this invariant both locally parameterises equivalence classes
of hyperbolic structures and is a complete invariant of the Dehn fillings of M
which admit a hyperbolic structure. We also give an explicit formula for the
ortholength invariant in terms of the traces of the holonomies of certain loops
in M. Conjecturally this new invariant is intimately related to the boundary of
the hyperbolic Dehn surgery space of M.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-23.abs.htm