VIRTUAL KNOT PRESENTATION OF RIBBON TORUS-KNOTS

By Shin Satoh. 2000

141 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2c589378d0afe23a81ccfd1f806022b4c7f63b96

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In Computational Theory and Mathematics

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Citations in the corpus

Finite-type invariants of w-knotted objects, I: w-knots and the Alexander polynomial (2014, methodology): “In Satoh [81], ı is called “Tube”.”
Knot Diagrammatics (2004, result): “This is related to observations by Silver and Williams [130], Manturov [103, 104] and by Satoh [126] showing that the fundamental group of a virtual knot can be interpreted as the fundamental group of the complement of a torus embedded in four dimensional Euclidean space.”
VIRTUAL BRAIDS AND THE L-MOVE (2005, background): “For reference to previous work on virtual links and braids the reader should consult [2, 6, 7, 9, 11, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 27, 28, 32, 36, 37].”
A journey through loop braid groups (2016, background): “We associate to it a symmetric braid broken surface diagram in the following way (see for details [44] and [52]).”
Virtual Braids (2004, background): “It is an open problem whether some of these counterexamples are isotopic to classical knots and links.”
Framed knot contact homology (2004, background): “In fact, they are invariants under a weaker equivalence, that of welded knots [18].”
Virtual knot theory-unsolved problems (2005, unknown): “…[23] [24] [25] [26] [31] [33] [34] [36] [37] [38] [39] [40] [41] [43] [50] [51] [55] [58] [59] [60] [61] [62] [64] [65] [67] [68] [70] [72] [73] [74] [75] [76] [78] [79] [80] [81] [82] [84] [86] [87] [88] [83] [90] [93] [94] [95] [96] [97] [98] [99] [100] [101] [102] [103] [104] [105] [106] [109].”