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.
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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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