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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2017.1
- 수록면
- 145 - 161 (17page)
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If a virtual knot diagram can be transformed to another virtual one by a finite sequence of crossing changes, Reidemeister moves and virtual moves then the two virtual knot diagrams are said to be \textit{homotopic}. There are infinitely many homotopy classes of virtual knot diagrams. We give necessary conditions by using polynomial invariants of virtual knots for two virtual knots to be homotopic.
For a sequence $S$ of crossing changes, Reidemeister moves and virtual moves between two homotopic virtual knot diagrams,we give a lower bound for the number of crossing changes in $S$ by using the affine index polynomial introduced in \cite{Kau4}. In \cite{Je4}, the first author gave the $q$-polynomial of a virtual knot diagram to find Reidemeister moves of virtually isotopic virtual knot diagrams.
We find how to apply Reidemeister moves by using the $q$-polynomial to show homotopy of two virtual knot diagrams.
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참고문헌 (21)
참고문헌 신청
A. Kawauchi / 2012 / On the Alexander polynomials of knots with Gordian distance one / Topology Appl. 159 : 948 ~ 958
C. Hayashi / 2006 / A lower bound for the number of Reidemeister moves for unknotting / J. Knot Theory Ramifications 15 (3) : 313 ~ 325
H. A. Dye / 2009 / Virtual crossing number and the arrow polynomial / J. Knot Theory Ramifications 18 (10) : 1335 ~ 1357
H. A. Dye / 2010 / Virtual homotopy / J. Knot Theory Ramifications 19 (7) : 935 ~ 960
L. H. Kauffman / 1999 / Virtual knot theory / Europ. J. Combin 20 : 663 ~ 690
C. Hayashi / 2006 / A lower bound for the number of Reidemeister moves for unknotting / J. Knot Theory Ramifications 15 (3) : 313 ~ 325
H. A. Dye / 2009 / Virtual crossing number and the arrow polynomial / J. Knot Theory Ramifications 18 (10) : 1335 ~ 1357
H. A. Dye / 2010 / Virtual homotopy / J. Knot Theory Ramifications 19 (7) : 935 ~ 960
L. H. Kauffman / 1999 / Virtual knot theory / Europ. J. Combin 20 : 663 ~ 690
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