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TWISTED FACE-PAIRING 3-MANIFOLDS WHICH ARE HYPERBOLIC

이경화|홍성복
대한수학회 (The Korean Mathematical Society)|2010.11|대한수학회보 (Bulletin of the KMS)|제47권 제6호|pp. 1297-1310

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참고문헌

키워드

twisted face-pairingfaceted 3-balltwisted face-pairing 3-manifoldsTakahashi manifolds
주제분류수학

초록

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.

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.

참고문헌 (12)

  1. R. Benedetti, "Lectures on Hyperbolic Geometry" (1992), Springer-Verlag
  2. J. W. Cannon, "Twisted face-pairing 3-manifolds", Trans. Amer. Math. Soc., 354(6), pp.2369~2397 (2002)
  3. J. W. Cannon, "Ample twisted face-pairing 3-manifolds, preprint", ~
  4. J. W. Cannon, "Heegaard diagrams and surgery descriptions for twisted face-pairing 3-mani-folds", Algebr. Geom. Topol., 3, pp.235~285 (2003)
  5. J. W. Cannon, "A survey of twisted face-pairing 3-manifolds, preprint", ~
  6. R. E. Gompf, "4-manifolds and Kirby Calculus" (1999), American Mathematical Society
  7. H. Helling, "On Fibonacci groups, preprint", ~
  8. M. Mulazzani, "On periodic Takahashi manifolds", Tsukuba J. Math., 25(2), pp.229~237 (2001)
  9. D. Rolfsen, "Knots and Links, Mathematics Lecture Series, No. 7" (1976), Publish or Perish, Inc.
  10. B. Ruini, "On the structure of Takahashi manifolds", Tsukuba J. Math., 22(3), pp.723~739 (1998)
  11. M. Takahashi, "On the presentations of the fundamental groups of 3-manifolds", Tsukuba J. Math., 13(1), pp.175~189 (1989)
  12. W. P. Thurston, "The geometry and topology of 3-manifold, Lect. Notes" (1980), Princeton Uni-versity

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