Homology 3-Spheres which are Obtained by Dehn Surgeries on Knots.
Kimihiko Motegi (1988)
Mathematische Annalen
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Kimihiko Motegi (1988)
Mathematische Annalen
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Paolo Lisca, Peter Ozsváth, András I. Stipsicz, Zoltán Szabó (2009)
Journal of the European Mathematical Society
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C.McA. Gordon, A.J. Casson (1983)
Inventiones mathematicae
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Steven A. Bleiler (1990)
Mathematische Annalen
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Ozsváth, Peter, Szabó, Zoltán (2003)
Geometry & Topology
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Roger Fenn, Louis H. Kauffman, Vassily O. Manturov (2005)
Fundamenta Mathematicae
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The present paper gives a quick survey of virtual and classical knot theory and presents a list of unsolved problems about virtual knots and links. These are all problems in low-dimensional topology with a special emphasis on virtual knots. In particular, we touch new approaches to knot invariants such as biquandles and Khovanov homology theory. Connections to other geometrical and combinatorial aspects are also discussed.
Plamenevskaya, Olga (2004)
Algebraic & Geometric Topology
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Szabó, Zoltán, Ozváth, Peter (2003)
Geometry & Topology
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J. Scott Carter, Mohamed Elhamdadi, Masahico Saito (2004)
Fundamenta Mathematicae
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A homology theory is developed for set-theoretic Yang-Baxter equations, and knot invariants are constructed by generalized colorings by biquandles and Yang-Baxter cocycles.
Susan Szczepanski (1989)
Inventiones mathematicae
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Livingston, Charles (2001)
Algebraic & Geometric Topology
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Livingston, Charles (2002)
Geometry & Topology
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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.
Francisco González-Acuña, Hamish Short (1991)
Revista Matemática de la Universidad Complutense de Madrid
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We study cyclic coverings of S3 branched over a knot, and study conditions under which the covering is a homology sphere. We show that the sequence of orders of the first homology groups for a given knot is either periodic of tends to infinity with the order of the covering, a result recently obtained independently by Riley. From our computations it follows that, if surgery on a knot k with less than 10 crossings produces a manifold with cyclic fundamental group, then k is a torus knot. ...