Invariants of Handlebody-Knots via Yokota's Invariants

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.

arXiv comment19 pages, the title was modified and typos were corrected

References in corpus (1)

• Observables in the Turaev-Viro and Crane-Yetter models

Cited by in corpus (1)

• Braided matter interactions in quantum gravity via 1-handle attachment