I describe how the colored Jones polynomials of the figure-eight knot determine the volumes of the three-manifolds obtained by Dehn surgeries along it, according to my joint work with Y. Yokota.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm184-0-15, author = {Hitoshi Murakami}, title = {The colored Jones polynomials of the figure-eight knot and the volumes of three-manifolds obtained by Dehn surgeries}, journal = {Fundamenta Mathematicae}, volume = {184}, year = {2004}, pages = {269-289}, zbl = {1095.57015}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm184-0-15} }
Hitoshi Murakami. The colored Jones polynomials of the figure-eight knot and the volumes of three-manifolds obtained by Dehn surgeries. Fundamenta Mathematicae, Tome 184 (2004) pp. 269-289. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm184-0-15/