Face pairing maps of Ford domains for cusped hyperbolic 3-manifolds
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We will describe a way to construct Ford domains of cusped hyperbolic 3-manifolds on maximal cusp diagrams and compute fundamental groups using face pairing maps as generators and Cannon-Floyd- Parry’s edge cycles as relations. We also describe explicitly a cutting and pasting alteration to reduce the number of faces on the bottom region of Ford domains. We expect that our analysis of Ford domains will be useful on other future research.
Abstract
We will describe a way to construct Ford domains of cusped hyperbolic 3-manifolds on maximal cusp diagrams and compute fundamental groups using face pairing maps as generators and Cannon-Floyd- Parry’s edge cycles as relations. We also describe explicitly a cutting and pasting alteration to reduce the number of faces on the bottom region of Ford domains. We expect that our analysis of Ford domains will be useful on other future research.
참고문헌 (5)
- C. Adams, "Hyperbolic invariants of knots and links", Transactions of the American Mathematical Society, 326(1), pp.1~56 (1991)
- P. J. Callahan, "A census of cusped hyperbolic 3-manifolds, With microfiche supplement", Mathematics of Computation, 68(225), pp.321~332 (1999)
- J. W. Cannon, "Introduction to twisted face-pairings", Mathematical Research Letters, 7(4), pp.477~491 (2000)
- N. M. Dunfield, "The virtual Haken conjecture: experiments and examples", Geometry & Topology, 7, pp.399~441 (2003)
- D. B. A. Epstein, "Euclidean decompositions of noncompact hyperbolic manifolds", Journal of Differential Geometry, 27(1), pp.67~80 (1988)