Straightening cell decompositions of cusped hyperbolic 3-manifolds

Marina Pescini

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1998)

  • Volume: 9, Issue: 2, page 101-109
  • ISSN: 1120-6330

Abstract

top
Let M be an oriented cusped hyperbolic 3-manifold and let τ be a topological ideal triangulation of M . We give a characterization for τ to be isotopic to an ideal geodesic triangulation; moreover we give a characterization for τ to flatten into a partially flat triangulation. Finally we prove that straightening combinatorially equivalent topological ideal cell decompositions gives the same geodesic decomposition, up to isometry.

How to cite

top

Pescini, Marina. "Straightening cell decompositions of cusped hyperbolic 3-manifolds." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 9.2 (1998): 101-109. <http://eudml.org/doc/252329>.

@article{Pescini1998,
abstract = {Let \( M \) be an oriented cusped hyperbolic 3-manifold and let \( \tau \) be a topological ideal triangulation of \( M \). We give a characterization for \( \tau \) to be isotopic to an ideal geodesic triangulation; moreover we give a characterization for \( \tau \) to flatten into a partially flat triangulation. Finally we prove that straightening combinatorially equivalent topological ideal cell decompositions gives the same geodesic decomposition, up to isometry.},
author = {Pescini, Marina},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Hyperbolic 3-manifolds; Flat triangulations; Ideal cell decompositions; ideal geodesic triangulation; flat triangulations},
language = {eng},
month = {6},
number = {2},
pages = {101-109},
publisher = {Accademia Nazionale dei Lincei},
title = {Straightening cell decompositions of cusped hyperbolic 3-manifolds},
url = {http://eudml.org/doc/252329},
volume = {9},
year = {1998},
}

TY - JOUR
AU - Pescini, Marina
TI - Straightening cell decompositions of cusped hyperbolic 3-manifolds
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1998/6//
PB - Accademia Nazionale dei Lincei
VL - 9
IS - 2
SP - 101
EP - 109
AB - Let \( M \) be an oriented cusped hyperbolic 3-manifold and let \( \tau \) be a topological ideal triangulation of \( M \). We give a characterization for \( \tau \) to be isotopic to an ideal geodesic triangulation; moreover we give a characterization for \( \tau \) to flatten into a partially flat triangulation. Finally we prove that straightening combinatorially equivalent topological ideal cell decompositions gives the same geodesic decomposition, up to isometry.
LA - eng
KW - Hyperbolic 3-manifolds; Flat triangulations; Ideal cell decompositions; ideal geodesic triangulation; flat triangulations
UR - http://eudml.org/doc/252329
ER -

References

top
  1. Benedetti, R. - Petronio, C., Lectures on Hyperbolic Geometry. Universitext, Springer-Verlag, Berlin-New York, 1992. Zbl0768.51018MR1219310DOI10.1007/978-3-642-58158-8
  2. Epstein, D. B. A. - Penner, R. C., Euclidean Decompositions of Noncompact Hyperbolic Manifolds. Journal Differential Geometry, 27, 1988, 67-80. Zbl0611.53036MR918457
  3. Petronio, C., Some remarks about straightening. Lectures given at Forschungsinstitut für Mathematik, ETH, Zürich, January 1994. 
  4. Sullivan, D., On the Ergodic Theory at Infinity of an Arbitrary Discrete Group of Hyperbolic Motions. In: I. Kra - B. Maskit (eds.), Riemann Surfaces and Related Topics. Ann. of Math. Studies, 97, Princeton Univ. Press, Princeton, NJ, 1981, 465-496. Zbl0567.58015MR624833

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.