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Finite Type Invariants and Virtual TwistMoves of Virtual Knots

Myeong-Ju Jeong
경북대학교 자연과학대학 수학과|2006.09|Kyungpook Mathematical Journal|제46권 제3호|pp. 449-461

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Abstract

Generalizing twist moves of classical knots, we introduce t(a1;    ; am)-moves of virtual knots for an m{tuple (a1;    ; am) of nonzero integers. In [4], M. Goussarov, M. Polyak and O. Viro introduced finite type invariants of virtual knots and Gauss diagram formulae giving combinatorial presentations of nite type invariants. By using the Gauss diagram formulae for the nite type invariants of degree 2, we give a necessary condition for a virtual long knot K to be transformed to a virtual long knot K0 by a nite sequence of t(a1;    ; am)-moves for an m-tuple (a1;    ; am) of nonzero integers with the same sign.

참고문헌 (13)

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관련 논문AI추천

Twist of Knots and the Q-polynomialsChan-young Park, Myeong-ju Jeong, Younhee Choi경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2004 · 제44권 제3호Virtual links with normal diagrams임영호영남수학회 · East Asian Mathematical Journal2009 · 제25권 제4호Finite Type Invariants and the Kauffman Bracket Polynomials of Virtual Knots박찬녕, 여순태, 정명주경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제4호The Forbidden Number of a KnotAlissa S. Crans, Blake Mellor, Sandy Ganzell경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제2호Polynomial Invariants for Virtual Knots via Virtualization Moves김세라, 임영호영남수학회 · East Asian Mathematical Journal2020 · 제36권 제5호On certain classes of links and $3$-manifolds김수환, 김양곡대한수학회 · 대한수학회논문집2005 · 제20권 제4호

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