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arXiv · 1112.2719

Invariants of Handlebody-Knots via Yokota's Invariants

Atsuhiko Mizusawa·Jun Murakami
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Abstract

We construct quantum $\mathcal{U}_q(\mathfrak{sl}_{\,2})$ type invariants for handlebody-knots in the 3-sphere $S^3$. 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.

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Atsuhiko Mizusawa, Jun Murakami. 2013-12-16. Invariants of Handlebody-Knots via Yokota's Invariants. https://doi.org/10.1142/s0218216513500685

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