Previously known algorithms to compute the symmetry group of a cusped
hyperbolic three-manifold and to test whether two cusped hyperbolic
three-manifolds are isometric do not apply directly to closed
manifolds. But by drilling out geodesics from closed manifolds one
may compute their symmetry groups and test for isometries using the
cusped manifold techniques. To do so, one must know precisely how
many geodesics of a given length the closed manifold has. Here we
prove the propositions needed to rigorously compute a length spectrum,
with multiplicities. We also tabulate the symmetry groups of the
smallest known closed hyperbolic three-manifolds.
@article{1048515809,
author = {Hodgson, Craig D. and Weeks, Jeffrey R.},
title = {Symmetries, isometries and length spectra of closed hyperbolic three-manifolds},
journal = {Experiment. Math.},
volume = {3},
number = {4},
year = {1994},
pages = { 261-274},
language = {en},
url = {http://dml.mathdoc.fr/item/1048515809}
}
Hodgson, Craig D.; Weeks, Jeffrey R. Symmetries, isometries and length spectra of closed hyperbolic three-manifolds. Experiment. Math., Tome 3 (1994) no. 4, pp. 261-274. http://gdmltest.u-ga.fr/item/1048515809/