Constructions of invariants for surface-links via link invariants and applications to the Kauffman bracket

Sang Youl Lee

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arXiv · 1609.09587

Constructions of invariants for surface-links via link invariants and applications to the Kauffman bracket

Sang Youl Lee

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Abstract

In this paper, we formulate a construction of ideal coset invariants for surface-links in $4$-space using invariants for knots and links in $3$-space. We apply the construction to the Kauffman bracket polynomial invariant and obtain an invariant for surface-links called the Kauffman bracket ideal coset invariant of surface-links. We also define a series of new invariants $\{{\mathbf K}_{2n-1}(\mathcal L) | n=2, 3, 4, \ldots\}$ for surface-links $\mathcal L$ by using skein relations, which are more effective than the Kauffman bracket ideal coset invariant to distinguish given surface-links.

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BibTeX RIS

Sang Youl Lee. 2016-09-30. Constructions of invariants for surface-links via link invariants and applications to the Kauffman bracket. https://arxiv.org/abs/1609.09587

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