Handlebody-knot invariants derived from unimodular Hopf algebras

Atsushi Ishii; Akira Masuoka

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arXiv · 1307.5632

Handlebody-knot invariants derived from unimodular Hopf algebras

Atsushi Ishii·Akira Masuoka

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Abstract

A handlebody-knot is a handlebody embedded in the 3-sphere. We establish a uniform method to construct invariants for handlebody-links. We introduce the category $\mathcal{T}$ of handlebody-tangles and present it by generators and relations. The result tells us that every functor on $\mathcal{T}$ that gives rise to invariants is derived from what we call a quantum-commutative quantum-symmetric algebra in the target category. The example of such algebras of our main concern is finite-dimensional unimodular Hopf algebras. We investigate how those Hopf algebras give rise to handlebody-knot invariants.

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BibTeX RIS

Atsushi Ishii, Akira Masuoka. 2013-07-22. Handlebody-knot invariants derived from unimodular Hopf algebras. https://arxiv.org/abs/1307.5632

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