2011
DOI: 10.1090/conm/541/10685
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An introduction to fully augmented links

Abstract: Abstract. In this article we summarize information on the class of fully augmented links. These links are geometrically explicit, and therefore provide a large class of examples of hyperbolic links for which geometric information can be computed.

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Cited by 25 publications
(36 citation statements)
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“…The link L is hyperbolic in M by [4], and Dehn filling each augmenting component of Q produces L. So, vol(M \ L) < vol(M \ Q) (for instance, see Theorem E.7.2 of [7]), and the lower volume bounds on alternating links from [16] and [12] apply to rubber band links in the thickened surface S × I. In the special case χ(S) ≥ 0, then lower bounds from [20] and [15] exploit the fact the augmented alternating link Q is fully augmented.…”
Section: Further Applicationsmentioning
confidence: 99%
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“…The link L is hyperbolic in M by [4], and Dehn filling each augmenting component of Q produces L. So, vol(M \ L) < vol(M \ Q) (for instance, see Theorem E.7.2 of [7]), and the lower volume bounds on alternating links from [16] and [12] apply to rubber band links in the thickened surface S × I. In the special case χ(S) ≥ 0, then lower bounds from [20] and [15] exploit the fact the augmented alternating link Q is fully augmented.…”
Section: Further Applicationsmentioning
confidence: 99%
“…The twice-punctured disks bounded by the edge components must intersect all of the totally geodesic surfaces on the projection surface in right angles. The link complement can be decomposed into two pieces, each of which is topologically a thickened surface but each of which has an ideal polygonal boundary on one side with all neighboring polygons meeting at right angles, as in the decompositions of fully augmented alternating links in the 3-sphere [20] and T × I [15]. Proof.…”
Section: Let Us Recall Theorem 13mentioning
confidence: 99%
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“…The geometry of augmented links, first studied by Adams [2], is well understood. Below, we will summarize some results and properties we need; for more details see Purcell's expository article [39] and references therein. We will consider the non-crossing circle components of L flat on the projection plane and the crossing circles bound crossing disks vertical to the projection plane.…”
Section: Augmented Links and Estimates With Normal Surfacesmentioning
confidence: 99%