Open Access
Translator Disclaimer
2002 A new invariant on hyperbolic Dehn surgery space
James G Dowty
Algebr. Geom. Topol. 2(1): 465-497 (2002). DOI: 10.2140/agt.2002.2.465


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.


Download Citation

James G Dowty. "A new invariant on hyperbolic Dehn surgery space." Algebr. Geom. Topol. 2 (1) 465 - 497, 2002.


Received: 24 October 2001; Revised: 24 May 2002; Accepted: 6 June 2002; Published: 2002
First available in Project Euclid: 21 December 2017

zbMATH: 0994.57017
MathSciNet: MR1917063
Digital Object Identifier: 10.2140/agt.2002.2.465

Primary: 57M50
Secondary: 57M27

Rights: Copyright © 2002 Mathematical Sciences Publishers


Vol.2 • No. 1 • 2002
Back to Top