Hitoshi Murakami

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We clarify and refine the relation between the asymptotic behavior of the colored Jones polynomial and Chern-Simons gauge theory with complex gauge group SL(2, C). The precise comparison requires a careful understanding of some delicate issues, such as normalization of the colored Jones polynomial and the choice of polarization in Chern-Simons theory.(More)
We define A k-moves for embeddings of a finite graph into the 3-sphere for each natural number k. Let A k-equivalence denote an equivalence relation generated by A k-moves and ambient isotopy. A k-equivalence implies A k−1-equivalence. Let F be an A k−1-equivalence class of the embeddings of a finite graph into the 3-sphere. Let G be the quotient set of F(More)
BACKGROUND Refusal of the oral polio vaccine (OPV) is a difficulty faced by the Polio Eradication Initiative (PEI) in multiple endemic areas, including the Khyber Pakhtunkhwa Province (KPP), Pakistan. In 2007, we investigated community perceptions of the OPV and estimated the prevalence of OPV refusal in three districts in Swat Valley, KPP, a polio-endemic(More)
R.M. Kashaev conjectured that the asymptotic behavior of his link invariant, which equals the colored Jones polynomial evaluated at a root of unity, determines the hyperbolic volume of any hyperbolic link complement. We observe numerically that for knots 6 3 , 8 9 and 8 20 and for the Whitehead link, the colored Jones polynomials are related to the(More)