Classification of ribbon 2-knots of 1-fusion with length up to six
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DOI: 10.1016/j.topol.2020.107521
Abstract: Abstract We classify oriented ribbon 2-knots of 1-fusion with length up to six. We show the difference by: the Alexander polynomial; the trace set, which is obtained from the representations of the knot group to… read more here.
Keywords: knots fusion; length six; fusion length; ribbon knots ... See more keywords
Enumeration of ribbon 2-knots presented by virtual arcs with up to four crossings
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DOI: 10.1142/s0218216517500420
Abstract: We enumerate ribbon 2-knots presented by virtual arc diagrams with up to four classical crossings. We use a linear Gauss diagram for a virtual arc diagram. read more here.
Keywords: presented virtual; enumeration ribbon; virtual arcs; knots presented ... See more keywords
Ribbon n-knots with isomorphic quandles
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DOI: 10.1142/s0218216519500433
Abstract: Let [Formula: see text] be ribbon knottings of [Formula: see text]-spheres or tori in [Formula: see text], [Formula: see text]. We show that if the knot quandles of these knots are isomorphic, then the ribbon… read more here.
Keywords: isomorphic quandles; ribbon knots; knots isomorphic; formula see ... See more keywords
Suciu’s ribbon 2-knots with isomorphic group
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DOI: 10.1142/s0218216520500534
Abstract: Suciu constructed infinitely many ribbon 2-knots in S4 whose knot groups are isomorphic to the trefoil knot group. They are distinguished by the second homotopy groups. We classify these knots by u... read more here.
Keywords: knots isomorphic; suciu ribbon; isomorphic group; knot ... See more keywords