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- Mutation_(knot_theory) abstract "In the mathematical field of knot theory, a mutation is an operation on a knot that can produce different knots. Suppose K is a knot given in the form of a knot diagram. Consider a disc D in the projection plane of the diagram whose boundary circle intersects K exactly four times. We may suppose that (after planar isotopy) the disc is geometrically round and the four points of intersection on its boundary with K are equally spaced. The part of the knot inside the disc is a tangle. There are two reflections that switch pairs of endpoints of the tangle. There is also a rotation that results from composition of the reflections. A mutation replaces the original tangle by a tangle given by any of these operations. The result will always be a knot and is called a mutant of K.Mutants can be difficult to distinguish as they have a number of the same invariants. They have the same hyperbolic volume (by a result of Ruberman), and have the same HOMFLY polynomials.".
- Mutation_(knot_theory) thumbnail Knudemutation.svg?width=300.
- Mutation_(knot_theory) wikiPageID "3727019".
- Mutation_(knot_theory) wikiPageLength "1647".
- Mutation_(knot_theory) wikiPageOutDegree "10".
- Mutation_(knot_theory) wikiPageRevisionID "704089698".
- Mutation_(knot_theory) wikiPageWikiLink Category:Knot_operations.
- Mutation_(knot_theory) wikiPageWikiLink HOMFLY_polynomial.
- Mutation_(knot_theory) wikiPageWikiLink Hyperbolic_link.
- Mutation_(knot_theory) wikiPageWikiLink Knot_operation.
- Mutation_(knot_theory) wikiPageWikiLink Knot_theory.
- Mutation_(knot_theory) wikiPageWikiLink Mathematics.
- Mutation_(knot_theory) wikiPageWikiLink Seifert_surface.
- Mutation_(knot_theory) wikiPageWikiLink Tangle_(mathematics).
- Mutation_(knot_theory) wikiPageWikiLink File:Knudemutation.svg.
- Mutation_(knot_theory) wikiPageWikiLinkText "Mutation (knot theory)".
- Mutation_(knot_theory) wikiPageWikiLinkText "mutants".
- Mutation_(knot_theory) wikiPageWikiLinkText "mutation (knot theory)".
- Mutation_(knot_theory) wikiPageWikiLinkText "mutation".
- Mutation_(knot_theory) wikiPageUsesTemplate Template:Knot_theory.
- Mutation_(knot_theory) wikiPageUsesTemplate Template:Knottheory-stub.
- Mutation_(knot_theory) wikiPageUsesTemplate Template:Reflist.
- Mutation_(knot_theory) subject Category:Knot_operations.
- Mutation_(knot_theory) hypernym Operation.
- Mutation_(knot_theory) type MilitaryConflict.
- Mutation_(knot_theory) comment "In the mathematical field of knot theory, a mutation is an operation on a knot that can produce different knots. Suppose K is a knot given in the form of a knot diagram. Consider a disc D in the projection plane of the diagram whose boundary circle intersects K exactly four times. We may suppose that (after planar isotopy) the disc is geometrically round and the four points of intersection on its boundary with K are equally spaced. The part of the knot inside the disc is a tangle.".
- Mutation_(knot_theory) label "Mutation (knot theory)".
- Mutation_(knot_theory) sameAs Q1955809.
- Mutation_(knot_theory) sameAs Mutation_(Knotentheorie).
- Mutation_(knot_theory) sameAs m.09xk2j.
- Mutation_(knot_theory) sameAs Мутация_(теория_узлов).
- Mutation_(knot_theory) sameAs Q1955809.
- Mutation_(knot_theory) wasDerivedFrom Mutation_(knot_theory)?oldid=704089698.
- Mutation_(knot_theory) depiction Knudemutation.svg.
- Mutation_(knot_theory) isPrimaryTopicOf Mutation_(knot_theory).