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...[a1]]], named by him complexions-symbol (cf. also [[Knot and link diagrams|Knot and link diagrams]]). Listing associated with every corner of a crossing a
3 KB (496 words) - 07:37, 18 March 2023
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...ed from it. The integral is defined for a knot $K$ (cf. also [[Knot theory|Knot theory]]) embedded in the three-dimensional space $ \mathbf{R} ^ { 3 } = \
10 KB (1,481 words) - 19:05, 23 January 2024
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* {{Ref|a2}} A. Kawauchi, "A survey of knot theory", Birkhäuser (1996) {{ZBL|0861.57001}}
2 KB (289 words) - 07:50, 25 November 2023
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...he Jones–Conway polynomial is usually normalized to be $1$ for the trivial knot. Then for the trivial link of $n$ components, $T _ { n }$, one gets
18 KB (2,713 words) - 05:14, 15 February 2024
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...lign="top"> K. Murasugi, "Jones polynomial and classical conjectures in knot theory" ''Topology'' , '''26''' : 2 (1987) pp. 187–194</td></tr><tr><
7 KB (1,054 words) - 07:42, 10 February 2024
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...e (notably, both left and right duals) one can arrange that every oriented
knot can be read from top to bottom as a morphism <img align="absmiddle" border=
17 KB (2,633 words) - 17:42, 1 July 2020
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...nts of knots, links or three-dimensional manifolds (cf. also [[Knot theory|Knot theory]]; [[Link|Link]]; [[Three-dimensional manifold|Three-dimensional man
19 KB (2,895 words) - 17:45, 1 July 2020
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...athematical problems in|Statistical mechanics]], network reliability and [[knot theory]]: Suppose $M$ is a probabilistic matroid, i.e., each $e \in E$ has
11 KB (1,736 words) - 06:27, 15 February 2024
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...knot invariants and invariants of three-manifolds (cf. also [[Knot theory|Knot theory]]; [[Three-dimensional manifold|Three-dimensional manifold]]), [[Qua
20 KB (2,919 words) - 00:57, 15 February 2024
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...d of algebra, in which the algebraic information is expressed by braid and knot diagrams. In effect, algebraic operations are implemented by "wiring up"
21 KB (3,130 words) - 17:42, 1 July 2020
the images of the simple roots $ \alpha _{i} \in \mathfrak h ^{*} $ .
...the Jones polynomial [[#References|[a9]]]. More precisely, to an oriented knot $ \gamma \subset \mathbf R ^{3} $
18 KB (2,674 words) - 19:09, 16 December 2019
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...reduced to the study of the asphericity of labelled oriented trees. Every knot group has a labelled oriented tree presentation (the Wirtinger presentation
31 KB (4,667 words) - 17:46, 1 July 2020
...t of these ideas the laws of Alexander duality and their generalization, [[knot theory]], were obtained.
...hing but topology. Some of this persists; geometric topology ranges from [[knot theory]] (which is not at all general topology) through $3$-dimensional top
38 KB (5,626 words) - 17:15, 20 March 2018