2017
DOI: 10.2140/agt.2017.17.2893
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Detecting essential surfaces as intersections in the character variety

Abstract: We describe a family of hyperbolic knots whose character variety contain exactly two distinct components of characters of irreducible representations. The intersection points between the components carry rich topological information. In particular, these points are non-integral and detect a Seifert surface.arXiv:1609.04780v2 [math.GT]

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Cited by 5 publications
(9 citation statements)
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“…Also, note that this presentation for the fundamental group comes from the two-bridge normal form for 7 4 , namely (15,11). These facts and the following are in [5], section 5.…”
Section: 2mentioning
confidence: 82%
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“…Also, note that this presentation for the fundamental group comes from the two-bridge normal form for 7 4 , namely (15,11). These facts and the following are in [5], section 5.…”
Section: 2mentioning
confidence: 82%
“…Remark 6.15 (Affine Intersection Points). Chu showed in [5] Section 5.1 that there are four affine points on the canonical component, C, for 7 4 which intersect the other component of the character variety containing the character of an irreducible representation. They lie in a number field L of degree 4.…”
Section: Torsion Pointsmentioning
confidence: 99%
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“…However, being Dehn fillings on a hand full of links, it is quick to check that the volumes for these examples are bounded by 7.4, while the volumes of 2-bridge links can be arbitrarily large. Nonetheless, including Riley's original results, these formulas have enjoyed a variety of applications including [5], [6], [11], [17], [18], [19], and [26].…”
Section: Introductionmentioning
confidence: 99%