Polynomial of an oriented surface-link diagram via quantum A2 invariantopen access
- Authors
- Joung, Yewon; Kamada, Seiichi; Kawauchi, Akio; Lee, Sang Youl
- Issue Date
- Oct-2017
- Publisher
- ELSEVIER SCIENCE BV
- Keywords
- Marked graph diagram; Ribbon marked graph; Surface-link; Quantum A(2) invariant; Tangled trivalent graph
- Citation
- TOPOLOGY AND ITS APPLICATIONS, v.231, pp.159 - 185
- Indexed
- SCIE
SCOPUS
- Journal Title
- TOPOLOGY AND ITS APPLICATIONS
- Volume
- 231
- Start Page
- 159
- End Page
- 185
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/192410
- DOI
- 10.1016/j.topol.2017.08.030
- ISSN
- 0166-8641
- 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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