Ideal triangulations of hyperbolic 3 -manifolds

Carlo Petronio

Bollettino dell'Unione Matematica Italiana (2000)

  • Volume: 3-B, Issue: 3, page 657-672
  • ISSN: 0392-4041

How to cite

top

Petronio, Carlo. "Ideal triangulations of hyperbolic $3$-manifolds." Bollettino dell'Unione Matematica Italiana 3-B.3 (2000): 657-672. <http://eudml.org/doc/195671>.

@article{Petronio2000,
author = {Petronio, Carlo},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {triangulation},
language = {eng},
month = {10},
number = {3},
pages = {657-672},
publisher = {Unione Matematica Italiana},
title = {Ideal triangulations of hyperbolic $3$-manifolds},
url = {http://eudml.org/doc/195671},
volume = {3-B},
year = {2000},
}

TY - JOUR
AU - Petronio, Carlo
TI - Ideal triangulations of hyperbolic $3$-manifolds
JO - Bollettino dell'Unione Matematica Italiana
DA - 2000/10//
PB - Unione Matematica Italiana
VL - 3-B
IS - 3
SP - 657
EP - 672
LA - eng
KW - triangulation
UR - http://eudml.org/doc/195671
ER -

References

top
  1. BENEDETTI, R.- PETRONIO, C., Lectures on Hyperbolic Geometry, Universitext, Springer-Verlag, Berlin-Heidelberg-New York, 1992. Zbl0768.51018MR1219310
  2. BOILEAU, M.- PORTI, J., Geometrization of 3-orbifolds of cyclic type, Preprint math- GT.9805073, 1998. MR1844891
  3. CASSON, A.- JUNGREIS, D., Convergence groups and Seifert fibered 3-manifolds, Invent. Math., 118 (1994), 441-456. Zbl0840.57005MR1296353
  4. EPSTEIN, D.- PENNER, R., Euclidean decomposition of non-compact hyperbolic manifolds, J. Differential Geom.27 (1988), 67-80. Zbl0611.53036MR918457
  5. EPSTEIN, D.- PETRONIO, C., An exposition of Poincaré's polyhedron theorem, Enseign. Math. (2), 40 (1994), 113-170. Zbl0808.52011MR1279064
  6. JACO, W.- SHALEN, P., Seifert fibered spaces in 3-manifolds, Memoirs of the Amer. Math. Soc. Vol. 220, Providence RI, 1979. Zbl0415.57005MR537728
  7. NEUMANN, W.- ZAGIER, D., Volumes of hyperbolic three-manifolds, Topology, 24 (1985), 307-332. Zbl0589.57015MR815482
  8. PESCINI, M., Straightening cell decompositions of cusped hyperbolic 3-manifolds, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 9 (1998), 101-109. Zbl0927.57012MR1677258
  9. PETRONIO, C.- PORTI, J., Negatively oriented ideal triangulations and a poof of Thurston's hyperbolic Dehn filling theorem, to appear in Expos. Math. Zbl0977.57011MR1751141
  10. PETRONIO, C.- WEEKS, J., Partially flat ideal triangulations of hyperbolic 3-manifolds, to appear in Osaka J. Math. Zbl0952.57003MR1772844
  11. ROLFSEN, D., Knots and Links, Math. Lecture Series Vol. 7, Publish or Perish, Berkeley CA, 1976. Zbl0339.55004MR515288
  12. SCOTT, P., The geometries of 3-manifolds, Bull. London Math. Soc., 15 (1983), 401-487. Zbl0561.57001MR705527
  13. SCOTT, P., Strong annulus and torus theorems and the enclosing property of characteristic submanifolds of 3-manifolds, Quart. J. Math. Oxford, 35 (1984), 485-506. Zbl0589.57006MR767777
  14. THURSTON, W., The Geometry and Topology of 3-manifolds, mimeographed notes, Princeton, 1979. 
  15. THURSTON, W., Three-dimensional manifolds, Kleinian groups, and hyperbolic geometry, Bull. Amer. Math. Soc., 6 (1982), 357-381. Zbl0496.57005MR648524
  16. THURSTON, W., Hyperbolic structures on 3-manifolds I: Deformations of acylindrical manifolds, Ann. of Math., 124 (1986), 203-246. Zbl0668.57015MR855294
  17. WADA, M.- YAMASHITA, Y.- YOSHIDA, H., An inequality for polyhedra and ideal triangulations of cusped hyperbolic 3-manifolds, Proc. Amer. Math. Soc., 124 (1996), 3905-3911. Zbl0866.57012MR1346992
  18. WEEKS, J., SnapPea, The hyperbolic structures computer program, available from www.northnet.org/weeks. 

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.