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THE JONES POLYNOMIAL AND THE INTERSECTION NUMBERS OF TWISTED CYCLES ASSOCIATED WITH A SELBERG TYPE INTEGRAL

KATSUHISA MIMACHI

Department of Mathematics, Tokyo Institute of Technology, Oh-Okayama, Meguro-Ku, Tokyo 152-8551, Japan

https://doi.org/10.1142/S0218216511008887Cited by:2 (Source: Crossref)

Abstract

We give a new definition of the Jones polynomial by means of the intersection number of loaded (or twisted) cycles associated with a Selberg type integral. Our definition is naturally formulated in the framework of the twisted homology theory, which is developd by Aomoto to study the special functions of hypergeometric type. The naturality of the definition leads to evaluate the Jones polynomials in several cases: well-known results in the case of two-bridge link, a formula for (3, s)-torus and that for the Prezel with 3 parameters. Our definition is motivated by the work of Bigelow.

Keywords:

AMSC: 57M27, 20F36, 33C60

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