1992
DOI: 10.1007/bf01232034
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Cusp structures of alternating links

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Cited by 24 publications
(41 citation statements)
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“…In [1], the class of well-balanced alternating links are shown to be almost cubed and so the corollary applies.…”
Section: Corollary 45 Suppose That M Is a Compact P 2 -Irreducible 3mentioning
confidence: 92%
“…In [1], the class of well-balanced alternating links are shown to be almost cubed and so the corollary applies.…”
Section: Corollary 45 Suppose That M Is a Compact P 2 -Irreducible 3mentioning
confidence: 92%
“…Let M=(T2×I)L be the link complement. The checkerboard polyhedral decomposition of the complement of an alternating link in S3, as in , can be generalized to that of an alternating link in T2×I. This was done for a single example in , and much more generally in .…”
Section: Torihedramentioning
confidence: 99%
“…It is well known, due to work of Menasco in the 1980s, that there exists a hyperbolic structure on the complement of any prime alternating link in S3 that is not a (2,q)‐torus link . The alternating diagram also provides a natural explicit decomposition of the link complement into two ideal checkerboard polyhedra with faces identified . Aitchison and Reeves studied alternating links for which these combinatorial polyhedra can be realized directly as ideal hyperbolic polyhedra that can be glued together to obtain the complete hyperbolic structure on the link complement.…”
Section: Introductionmentioning
confidence: 99%
“…Their bounds on |q| are a little stronger than those in Theorem 5.1, but their arguments only seem to work for embedded surfaces, and therefore do not imply that the fundamental group of the filled-in 3-manifold is infinite and word hyperbolic. Aitchison, Lumsden and Rubinstein [3] studied certain classes of alternating links and demonstrated the existence of non-positively curved metrics on their exteriors. Our approach is perhaps closest in spirit to theirs, but there is very little overlap in our results.…”
Section: Introductionmentioning
confidence: 99%