Faithful equivalence of equivalent ribbon surface-links
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DOI: 10.1142/s0218216518430034
Abstract: A chord graph in 3-space is constructed from a ribbon surface-link in 4-space. In earlier papers, the three moves on the diagrams of chord graphs (namely, the chord diagrams) were introduced to des... read more here.
Keywords: faithful equivalence; surface; surface links; ribbon surface ... See more keywords
Biquandle cohomology and state-sum invariants of links and surface-links
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DOI: 10.1142/s0218216518430162
Abstract: In this paper, we discuss the (co)homology theory of biquandles, derived biquandle cocycle invariants for oriented surface-links using broken surface diagrams and how to compute the biquandle cocycle invariants from marked graph diagrams. We also… read more here.
Keywords: state sum; cohomology state; cocycle invariants; surface links ... See more keywords
Presentation of immersed surface-links by marked graph diagrams
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DOI: 10.1142/s0218216518500529
Abstract: It is well known that surface-links in [Formula: see text]-space can be presented by diagrams on the plane of [Formula: see text]-valent spatial graphs with makers on the vertices, called marked graph diagrams. In this… read more here.
Keywords: graph diagrams; surface; surface links; immersed surface ... See more keywords
On the Triple Point Number of Surface-Links in Yoshikawa's Table
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DOI: 10.1142/s0218216523500372
Abstract: Yoshikawa made a table of knotted surfaces in R^4 with ch-index 10 or less. This remarkable table is the first to enumerate knotted surfaces analogous to the classical prime knot table. A broken sheet diagram… read more here.
Keywords: surface links; triple point; point number; surface ... See more keywords