# Invariants of handlebody-knots via yokota's invariants

Atsuhiko Mizusawa, Jun Murakami

Research output: Contribution to journalArticle

2 Citations (Scopus)

### Abstract

We construct quantum $\mathcal{U}-q(\mathfrak{sl}-{2})$ 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.

Original language English 1350068 Journal of Knot Theory and its Ramifications 22 11 https://doi.org/10.1142/S0218216513500685 Published - 2013 Oct

### Fingerprint

Handlebody
Knot
Invariant
Kauffman Bracket
Spatial Graph
Colored Graph
Table
Genus

### Keywords

• Handlebody-knot
• quantum invariant
• WRT invariants
• Yokota's invariants

### ASJC Scopus subject areas

• Algebra and Number Theory

### Cite this

Invariants of handlebody-knots via yokota's invariants. / Mizusawa, Atsuhiko; Murakami, Jun.

In: Journal of Knot Theory and its Ramifications, Vol. 22, No. 11, 1350068, 10.2013.

Research output: Contribution to journalArticle

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