JOURNAL BROWSE
Search
Advanced SearchSearch Tips
TWISTED FACE-PAIRING 3-MANIFOLDS WHICH ARE HYPERBOLIC
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
TWISTED FACE-PAIRING 3-MANIFOLDS WHICH ARE HYPERBOLIC
Hong, Sung-Bok; Lee, Kyung-Hwa;
  PDF(new window)
 Abstract
We construct a family of 3-balls using cones which represent closed orientable 3-manifolds and study twisted face-pairing construction due to Cannon, Floyd and Parry to understand the structure of such manifolds. Moreover, we prove that those manifolds are hyperbolic.
 Keywords
twisted face-pairing;faceted 3-ball;twisted face-pairing 3-manifolds;Takahashi manifolds;
 Language
English
 Cited by
 References
1.
R. Benedetti and C. Petronio, Lectures on Hyperbolic Geometry, Springer-Verlag, Berlin-Heidelberg-New York, 1992.

2.
J. W. Cannon, W. J. Floyd, and W. R. Parry, Twisted face-pairing 3-manifolds, Trans. Amer. Math. Soc. 354 (2002), no. 6, 2369-2397. crossref(new window)

3.
J. W. Cannon, W. J. Floyd, and W. R. Parry, Ample twisted face-pairing 3-manifolds, preprint.

4.
J. W. Cannon, W. J. Floyd, and W. R. Parry, Heegaard diagrams and surgery descriptions for twisted face-pairing 3-manifolds, Algebr. Geom. Topol. 3 (2003), 235-285. crossref(new window)

5.
J. W. Cannon, W. J. Floyd, and W. R. Parry, A survey of twisted face-pairing 3-manifolds, preprint.

6.
R. E. Gompf and A. I. Stipsicz, 4-manifolds and Kirby Calculus, Graduate Studies in Mathematics, 20. American Mathematical Society, Providence, RI, 1999.

7.
H. Helling, A. C. Kim, and J. Mennicke, On Fibonacci groups, preprint.

8.
M. Mulazzani, On periodic Takahashi manifolds, Tsukuba J. Math. 25 (2001), no. 2, 229-237. crossref(new window)

9.
D. Rolfsen, Knots and Links, Mathematics Lecture Series, No. 7. Publish or Perish, Inc., Berkeley, Calif., 1976.

10.
B. Ruini and F. Spaggiari, On the structure of Takahashi manifolds, Tsukuba J. Math. 22 (1998), no. 3, 723-739. crossref(new window)

11.
M. Takahashi, On the presentations of the fundamental groups of 3-manifolds, Tsukuba J. Math. 13 (1989), no. 1, 175-189. crossref(new window)

12.
W. P. Thurston, The geometry and topology of 3-manifold, Lect. Notes, Princeton University, N. J., 1980.