TY - CHAP

T1 - Applications

AU - Futer, David

AU - Kalfagianni, Efstratia

AU - Purcell, Jessica

PY - 2013/1/1

Y1 - 2013/1/1

N2 - In this chapter, we will use the calculations of S3\\SA 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.

AB - In this chapter, we will use the calculations of S3\\SA 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.

KW - Colored Jones Polynomial

KW - Early Chapter

KW - Incompressible Surface

KW - Jones Polynomial

KW - Ricci Flow

UR - http://www.scopus.com/inward/record.url?scp=85072845127&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-33302-6_9

DO - 10.1007/978-3-642-33302-6_9

M3 - Chapter (Book)

AN - SCOPUS:85072845127

SN - 9783642333019

T3 - Lecture Notes in Mathematics

SP - 139

EP - 154

BT - Guts of Surfaces and the Colored Jones Polynomial

PB - Springer-Verlag London Ltd.

ER -