On maximal fibred submanifolds of a knot exterior.
Osamu Kakimizu (1989)
Mathematische Annalen
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Osamu Kakimizu (1989)
Mathematische Annalen
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Clark, Bradd Evans (1978)
International Journal of Mathematics and Mathematical Sciences
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Seiichi Kamada (2001)
Fundamenta Mathematicae
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A Wirtinger presentation of a knot group is obtained from a diagram of the knot. T. Yajima showed that for a 2-knot or a closed oriented surface embedded in the Euclidean 4-space, a Wirtinger presentation of the knot group is obtained from a diagram in an analogous way. J. S. Carter and M. Saito generalized the method to non-orientable surfaces in 4-space by cutting non-orientable sheets of their diagrams by some arcs. We give a modification to their method so that one does not need...
Livingston, Charles (2004)
Geometry & Topology
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Ronald Fintushel, Ronald J. Stern (1980)
Mathematische Zeitschrift
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S. Jablan, R. Sazdanovic (2003)
Visual Mathematics
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Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
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Kai Ishihara, Atsushi Ishii (2012)
Fundamenta Mathematicae
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A handlebody-knot is a handlebody embedded in the 3-sphere. We improve Luo's result about markings on a surface, and show that an IH-move is sufficient to investigate handlebody-knots with spatial trivalent graphs without cut-edges. We also give fundamental moves with a height function for handlebody-tangles, which helps us to define operator invariants for handlebody-knots. By using the fundamental moves, we give an operator invariant.
Denis Petrovich Ilyutko, Vassily Olegovich Manturov, Igor Mikhailovich Nikonov (2014)
Banach Center Publications
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In [12, 15] it was shown that in some knot theories the crucial role is played by parity, i.e. a function on crossings valued in {0,1} and behaving nicely with respect to Reidemeister moves. Any parity allows one to construct functorial mappings from knots to knots, to refine many invariants and to prove minimality theorems for knots. In the present paper, we generalise the notion of parity and construct parities with coefficients from an abelian group rather than ℤ₂ and investigate...
Roger Fenn, Denis P. Ilyutko, Louis H. Kauffman, Vassily O. Manturov (2014)
Banach Center Publications
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This paper is a concise introduction to virtual knot theory, coupled with a list of research problems in this field.
C. Kearton, E. Bayer-Fluckiger (1989)
Mathematische Zeitschrift
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Corinne Cerf (2002)
Visual Mathematics
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Richard Hartley (1980)
Mathematische Zeitschrift
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Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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Steven P. Plotnick (1983)
Mathematische Zeitschrift
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