A new invariant on hyperbolic Dehn surgery space

Details A new invariant on hyperbolic Dehn surgery space A new invariant on hyperbolic Dehn surgery space

2002-07-05

arxiv.org/abs/math/0207060v1

Algebr. Geom. Topol. 2 (2002) 465-497

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-23.abs.html

Scientific paper

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.

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