2016/06/01 by Murakami, Hiroki
#FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1606.00125
The "color" in the colored Jones polynomial is an integer parameter. In this paper, a periodic pattern of the values of the colored Jones polynomial at the second and the third roots of unity is found. If we substitute -1 to the colored Jones polynomial, the value is alternately 1 or the determinant of the given link. When it comes to substituting the primitive third root of unity, another periodic pattern appears.