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Displaying 1561 – 1580 of 1631

Winding Numbers on Surfaces II. Applications.

D.R.J. Chillingworth (1972)

Mathematische Annalen

Wirtinger presentations for higher dimensional manifold knots obtained from diagrams

Seiichi Kamada (2001)

Fundamenta Mathematicae

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 to find and...

Witten's conjecture and Property P.

Kronheimer, P.B., Mrowka, T.S. (2004)

Geometry & Topology

Yamada polynomial and crossing number of spatial graphs.

Tomoe Motohashi, Yoshiyuki Ohyama, Kouki Taniyama (1994)

Revista Matemática de la Universidad Complutense de Madrid

In this paper we estimate the crossing number of a flat vertex graph in 3-space in terms of the reduced degree of its Yamada polynomial.

Yang-Baxter deformations of quandles and racks.

Eisermann, Michael (2005)

Algebraic & Geometric Topology

$Z_{n}$ -actions on 3-manifolds

Józef H. Przytycki (1982)

Colloquium Mathematicae

Zeros of the Jones polynomial are dense in the complex plane.

Jin, Xian'an, Zhang, Fuji, Dong, Fengming, Tay, Eng Guan (2010)

The Electronic Journal of Combinatorics [electronic only]

Zur Faserung von Graphenmannigfaltigkeiten.

Aois Scharf (1975)

Mathematische Annalen

Zur Theorie massiver Knoten

O. KRÖTENHEERDT, S. VEIT (1976)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

$θ$ -curves inducing two different knots with the same $2$ -fold branched covering spaces

Soo Hwan Kim, Yangkok Kim (2003)

Bollettino dell'Unione Matematica Italiana

For a knot $K$ with a strong inversion $i$ induced by an unknotting tunnel, we have a double covering projection $Π : S^{3} \to S^{3} / i$ branched over a trivial knot $Π (fix (i))$ , where $fix (i)$ is the axis of $i$ . Then a set $Π (fix (i) \cup K)$ is called a $θ$ -curve. We construct $θ$ -curves and the $Z_{2} \oplus Z_{2}$ cyclic branched coverings over $θ$ -curves, having two non-isotopic Heegaard decompositions which are one stable equivalent.