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Displaying 181 – 200 of 643

Finite type invariants of integral homology 3-spheres: A survey

Xiao-Song Lin (1998)

Banach Center Publications

Flat hierarchy

Vassily O. Manturov (2005)

Fundamenta Mathematicae

We consider the hierarchy flats, a combinatorial generalization of flat virtual links proposed by Louis Kauffman. An approach to constructing invariants for hierarchy flats is presented; several examples are given.

Flows on $S^{3}$ supporting all links as orbits.

Ghrist, Robert W. (1995)

Electronic Research Announcements of the American Mathematical Society [electronic only]

Fox's congruence classes and the quantum-SU(2) invariants of links in 3-manifolds.

Marc Lackenby (1996)

Commentarii mathematici Helvetici

Framed holonomic knots.

Ekholm, Tobias, Wolff, Maxime (2002)

Algebraic & Geometric Topology

Framed Links for Pfeiffer Identities.

Allan J. Sieradski (1980)

Mathematische Zeitschrift

Free group automorphisms, invariant orderings and topological applications.

Rolfsen, Dale, Wiest, Bert (2001)

Algebraic & Geometric Topology

Frobenius algebras and skein modules of surfaces in 3-manifolds

Uwe Kaiser (2009)

Banach Center Publications

For each (commutative) Frobenius algebra there is defined a skein module of surfaces embedded in a given 3-manifold and bounding a prescribed curve system in the boundary. The skein relations are local and generate the kernel of a certain natural extension of the corresponding topological quantum field theory. In particular the skein module of the 3-ball is isomorphic to the ground ring of the Frobenius algebra. We prove a presentation theorem for the skein module with generators incompressible...

Generalized Chern-Simons theory and skein relations in arbitrary dimensions

Broda, B. (1993)

Proceedings of the Winter School "Geometry and Topology"

Generalized Montesinos knots, tunnels and N-torsion.

Yoav Moriah, Martin Lustig (1993)

Mathematische Annalen

Generalized n-colorings of links

Daniel Silver, Susan Williams (1998)

Banach Center Publications

The notion of an (n,r)-coloring for a link diagram generalizes the idea of an n-coloring introduced by R. H. Fox. For any positive integer n the various (n,r)-colorings of a diagram for an oriented link l correspond in a natural way to the periodic points of the representation shift $Φ_{/ n} (l)$ of the link. The number of (n,r)-colorings of a diagram for a satellite knot is determined by the colorings of its pattern and companion knots together with the winding number.

Generic immersions of curves, knots, monodry and Gordian number

Norbert A'Campo (1998)

Publications Mathématiques de l'IHÉS

Genus 2 Heegaard decompositions of small Seifert manifolds

Michel Boileau, D. J. Collins, H. Zieschang (1991)

Annales de l'institut Fourier

The genus 2 Heegaard splittings and decompositions of Seifert manifolds over $S$ with 3 exeptional fibres are classified with respect to isotopies and homeomorphisms. In general there are 3 different isotopy classes of Heegaard splittings and 6 different isotopy classes of Heegaard decompositions. Moreover, we determine when a homeomorphism class is not an isotopy class.

Geodesic knots in the figure-eight knot complement.

Miller, Sally M. (2001)

Experimental Mathematics

Geodesic surfaces in knot complements.

Aitchison, Iain R., Rubinstein, J.Hyam (1997)

Experimental Mathematics

Geometric invariants of link cobordism.

Tim D. Cochran (1985)

Commentarii mathematici Helvetici

Geometric presentations of classical knot groups.

Erbland, John, Guterriez, Mauricio (1991)

International Journal of Mathematics and Mathematical Sciences

Geometric types of twisted knots

Mohamed Aït-Nouh, Daniel Matignon, Kimihiko Motegi (2006)

Annales mathématiques Blaise Pascal

Let $K$ be a knot in the $3$ -sphere $S^{3}$ , and $Δ$ a disk in $S^{3}$ meeting $K$ transversely in the interior. For non-triviality we assume that $| Δ \cap K | \geq 2$ over all isotopies of $K$ in $S^{3} - \partial Δ$ . Let $K_{Δ, n}$ ( $\subset S^{3}$ ) be a knot obtained from $K$ by $n$ twistings along the disk $Δ$ . If the original knot is unknotted in $S^{3}$ , we call $K_{Δ, n}$ a twisted knot. We describe for which pair $(K, Δ)$ and an integer $n$ , the twisted knot $K_{Δ, n}$ is a torus knot, a satellite knot or a hyperbolic knot.

Geometrically fibred two-knots.

J.A. Hillman, S.P. Plotnick (1990)

Mathematische Annalen

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