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Applications

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2069)

Abstract

In this chapter, we will use the calculations of \(\mathrm{guts}({S}^{3}\setminus \setminus {S}_{A})\) obtained in earlier chapters to relate the geometry of A-adequate links to diagrammatic quantities and to Jones polynomials. In Sect. 9.1, we combine Theorem 5.14 with results of Agol et al. [6] to obtain bounds on the volumes of hyperbolic A-adequate links. A sample result is Theorem 9.7, which gives tight diagrammatic estimates on the volumes of positive braids with at least 3 crossings per twist region. The gap between the upper and lower bounds on volume is a factor of about 4.15.

Keywords

  • Ricci Flow
  • Jones Polynomial
  • Incompressible Surface
  • Early Chapter
  • Colored Jones Polynomial

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Fig. 9.1
Fig. 9.2
Fig. 9.3

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Futer, D., Kalfagianni, E., Purcell, J. (2013). Applications. In: Guts of Surfaces and the Colored Jones Polynomial. Lecture Notes in Mathematics, vol 2069. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33302-6_9

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