Geometric presentations of classical knot groups.
Erbland, John, Guterriez, Mauricio (1991)
International Journal of Mathematics and Mathematical Sciences
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Erbland, John, Guterriez, Mauricio (1991)
International Journal of Mathematics and Mathematical Sciences
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Akira Yasuhara (1992)
Revista Matemática de la Universidad Complutense de Madrid
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We investigate the knots in the boundary of the punctured complex projective plane. Our result gives an affirmative answer to a question raised by Suzuki. As an application, we answer to a question by Mathieu.
Vaughan Jones, Józef Przytycki (1998)
Banach Center Publications
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We show that Lissajous knots are equivalent to billiard knots in a cube. We consider also knots in general 3-dimensional billiard tables. We analyse symmetry of knots in billiard tables and show in particular that the Alexander polynomial of a Lissajous knot is a square modulo 2.
Barry Mazur (1959)
Publications Mathématiques de l'IHÉS
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Clark, Bradd Evans (1983)
International Journal of Mathematics and Mathematical Sciences
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Greene, Michael, Wiest, Bert (1998)
Geometry & Topology
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Akiko Shima (1998)
Revista Matemática Complutense
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Let T be a torus in S4 and T* a projection of T. If the singular set Gamma(T*) consists of one disjoint simple closed curve, then T can be moved to the standard position by an ambient isotopy of S4.
Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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Silver, Daniel S., Whitten, Wilbur (2005)
Algebraic & Geometric Topology
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Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
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Gabriela Hinojosa, Alberto Verjovsky (2006)
Revista Matemática Complutense
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In this paper we prove that a wild knot K which is the limit set of a Kleinian group acting conformally on the unit 3-sphere, with its standard metric, is homogeneous: given two points p, q ∈ K, there exists a homeomorphism f of the sphere such that f(K) = K and f(p) = q. We also show that if the wild knot is a fibered knot then we can choose an f which preserves the fibers.