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Polynomial Invariants for Virtual Knots via Virtualization Moves
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초록
We investigate some polynomial invariants for virtual knots via virtualization moves. We define two types of polynomials WG(t) and SG2 (t) from the definition of the index polynomial for virtual knots. And we show that they are invariants for virtual knots on the quotient ring Z[t±1]/I where I is an ideal generated by t2 − 1.
Abstract
We investigate some polynomial invariants for virtual knots via virtualization moves. We define two types of polynomials WG(t) and SG2 (t) from the definition of the index polynomial for virtual knots. And we show that they are invariants for virtual knots on the quotient ring Z[t±1]/I where I is an ideal generated by t2 − 1.
참고문헌 (6)
- Heather A. Dye, "An Invitation to Knot Theory: Virtual and Classical"
- M. Goussarov, "Finite type invariants of classical and virtual knots", Topology, 39, pp.1045~1068 (2000)
- Y. H. Im, "A sequence of polynomial invariants for Gauss diagrams", J. Knot Theory Ramifications, 26(7), pp.1750039~ (2017)
- K. Lee, "State sum invariants for flat virtual links using the flat intersection indices", ~
- L. H. Kauffman, "Virtual knot theory", European J. Combin, 20, pp.663~690 (1999)
- M. Polyak, "Minimal generating sets of Reidemeister moves", Quantum Topology, 1, pp.399~411 (2010)
관련 논문AI추천
Polynomial invariants of long virtual knots김세라, 임영호영남수학회 · East Asian Mathematical Journal2019 · 제35권 제1호Generalized Alexander Polynomial for Virtual Links via Parity김세라, 김준오영남수학회 · East Asian Mathematical Journal2025 · 제41권 제5호Polynomials and Homotopy of Virtual Knot Diagrams박맹상, 박찬녕, 정명주경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2017 · 제57권 제1호Delta Moves and Arrow Polynomials of Virtual Knots박찬녕, 정명주경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2018 · 제58권 제1호The Second Reidemeister Moves and Colorings of Virtual Knot Diagrams김윤재, 정명주경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2022 · 제62권 제2호VARIATIONS IN WRITHES OF VIRTUAL KNOTS UNDER A LOCAL MOVEAmrendra Gill, Prabhakar Madeti대한수학회 · 대한수학회보2022 · 제59권 제2호
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