Polynomial of an oriented surface-link diagram via quantum A_2 invariant

Yewon Joung; Seiichi Kamada; Akio Kawauchi; Sang Youl Lee

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arXiv · 1602.01558

Polynomial of an oriented surface-link diagram via quantum A_2 invariant

Yewon Joung·Seiichi Kamada·Akio Kawauchi·Sang Youl Lee

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Abstract

It is known that every surface-link can be presented by a marked graph diagram, and such a diagram presentation is unique up to moves called Yoshikawa moves. G. Kuperberg introduced a regular isotopy invariant, called the quantum A_2 invariant, for tangled trivalent graph diagrams. In this paper, a polynomial for a marked graph diagram is defined by use of the quantum A_2 invariant and it is studied how the polynomial changes under Yoshikawa moves. The notion of a ribbon marked graph is introduced to show that this polynomial is useful for an invariant of a ribbon 2-knot.

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Yewon Joung, Seiichi Kamada, Akio Kawauchi, Sang Youl Lee. 2016-02-04. Polynomial of an oriented surface-link diagram via quantum A_2 invariant. https://arxiv.org/abs/1602.01558

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