The Groups G2
                n
               with Additional Structures

Kim, Seongjeong

doi:10.1134/s0001434618030264

Cited by 2 publications

(5 citation statements)

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“…In [1], the author constructed knots in S g ×S 1 and local moves. In [2], the author defined "labels" of crossings of knots in S g × S 1 and its applications.…”

Section: Figure 1 Generalized Reidemeister Movesmentioning

confidence: 99%

“…This paper is contributed to expand the notion of "labels" of crossings of knots in S g × S 1 . In Section 2, we introduce basic notions of links in S g × S 1 and labels of crossings of knots in S g × S 1 .…”

Section: Figure 1 Generalized Reidemeister Movesmentioning

confidence: 99%

“…Theorem 2.3 (M. K. Dabkowski, M. Mroczkowski (2009) [9], Kim (2018) [1]). Let L and L be two links in S g × S 1 .…”

Section: Figure 1 Generalized Reidemeister Movesmentioning

confidence: 99%

“…More precisely, we consider the natural covering Π : R → S 1 defined by Π(r) = e 2πri . Then the function Id Sg ×Π : S g ×R → S g ×S 1 is also a covering over S g × S 1 where Id Sg : S g → S g is the identity map.…”

Section: Figure 1 Generalized Reidemeister Movesmentioning

confidence: 99%

“…In this paper we extend this notion more generally and discuss its geometrical meaning. This paper follows from [1].…”

mentioning

confidence: 99%

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Knots in $S_{g} \times S^{1}$ and winding parities

Kim¹

2021

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A virtual knot, which is one of generalizations of knots in R 3 (or S 3 ), is, roughly speaking, an embedded circle in thickened surface Sg × I. In this talk we will discuss about knots in 3 dimensional Sg × S 1 . We introduce basic notions for knots in Sg × S 1 , for example, diagrams, moves for diagrams and so on. For knots in Sg × S 1 technically we lose over/under information, but we have information "how many times a half of the crossing of the knot in Sg × S 1 rotates along S 1 ", we call it labels of crossings. In this paper we extend this notion more generally and discuss its geometrical meaning. This paper follows from [1].

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“…In [1], the author constructed knots in S g ×S 1 and local moves. In [2], the author defined "labels" of crossings of knots in S g × S 1 and its applications.…”

Section: Figure 1 Generalized Reidemeister Movesmentioning

confidence: 99%

Section: Figure 1 Generalized Reidemeister Movesmentioning

confidence: 99%

“…Theorem 2.3 (M. K. Dabkowski, M. Mroczkowski (2009) [9], Kim (2018) [1]). Let L and L be two links in S g × S 1 .…”

Section: Figure 1 Generalized Reidemeister Movesmentioning

confidence: 99%

Section: Figure 1 Generalized Reidemeister Movesmentioning

confidence: 99%

“…In this paper we extend this notion more generally and discuss its geometrical meaning. This paper follows from [1].…”

mentioning

confidence: 99%