arXiv subjects

Hiroki Murakami

Publications and source records attributed to Hiroki Murakami.

2 recordsLinked to original sources

arXiv2016

Periodicity Properties of the Colored Jones Polynomial

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.

math.GT↗

arXiv2016

A Note on Alternating Links and Root Polytopes

In this paper, a relationship between the determinant of an alternating link and a certain polytope obtained from the link diagram is analyzed. We also show that when the underlying graph of the link diagram is properly oriented, the number of its spanning arborescence is equal to the determinant, i.e., the value at -1 of the Jones polynomial.

math.GT↗