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INVARIANTS OF HANDLEBODY-KNOTS VIA YOKOTA'S INVARIANTS

Department of Mathematics, Fundamental Science and Engineering, Waseda University, 3-4-1Okubo, Shinjuku-ku, Tokyo 169-8555, Japan

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and

JUN MURAKAMI

Department of Mathematics, Fundamental Science and Engineering, Waseda University, 3-4-1Okubo, Shinjuku-ku, Tokyo 169-8555, Japan

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https://doi.org/10.1142/S0218216513500685Cited by:5 (Source: Crossref)

Abstract

We construct quantum type invariants for handlebody-knots in the 3-sphere S³. A handlebody-knot is an embedding of a handlebody in a 3-manifold. These invariants are linear sums of Yokota's invariants for colored spatial graphs which are defined by using the Kauffman bracket. We give a table of calculations of our invariants for genus 2 handlebody-knots up to six crossings. We also show our invariants are identified with special cases of the Witten–Reshetikhin–Turaev invariants.

Keywords:

AMSC: 57M27, 57M25, 57R65

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