Algebraic and Geometric Topology 2 (2002),
paper no. 23, pages 465-497.
A new invariant on hyperbolic Dehn surgery space
James G. Dowty
Abstract.
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.
Keywords.
Hyperbolic cone-manifolds, character variety, ortholengths
AMS subject classification.
Primary: 57M50.
Secondary: 57M27.
DOI: 10.2140/agt.2002.2.465
E-print: arXiv:math.GT/0207060
Submitted: 24 October 2001.
(Revised: 24 May 2002.)
Accepted: 6 June 2002.
Published: 22 June 2002.
Notes on file formats
James G. Dowty
Department of Mathematics, University of Melbourne
Parkville, 3052, Australia
Email: jamesdowty@bigpond.com.au
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