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- Alexanders_theorem abstract "In mathematics Alexander's theorem states that every knot or link can be represented as a closed braid. The theorem is named after James Waddell Alexander II, who published its proof in 1923.Braids were first considered as a tool of knot theory by Alexander. His theorem gives a positive answer tois it always possible to transform a given knot into a closed braid?However, the correspondence between knots and braids is clearly not one-to-one: a knot may have many braid representations. For example, conjugate braids yield equivalent knots. This leads to a second fundamental question:which closed braids represent the same knot type?That question is addressed in Markov's theorem, which gives ‘moves’ relating any two closed braids that represent the same knot.".
- Alexanders_theorem wikiPageExternalLink books?id=BewrZeACVKcC&pg=PA17.
- Alexanders_theorem wikiPageID "45513201".
- Alexanders_theorem wikiPageLength "1380".
- Alexanders_theorem wikiPageOutDegree "7".
- Alexanders_theorem wikiPageRevisionID "657240582".
- Alexanders_theorem wikiPageWikiLink Bijection.
- Alexanders_theorem wikiPageWikiLink Braid_theory.
- Alexanders_theorem wikiPageWikiLink Category:Knot_theory.
- Alexanders_theorem wikiPageWikiLink James_Waddell_Alexander_II.
- Alexanders_theorem wikiPageWikiLink Knot_(mathematics).
- Alexanders_theorem wikiPageWikiLink Knot_theory.
- Alexanders_theorem wikiPageWikiLink Link_(knot_theory).
- Alexanders_theorem wikiPageWikiLinkText "Alexander's theorem".
- Alexanders_theorem wikiPageWikiLinkText "theorem of Alexander's".
- Alexanders_theorem hasPhotoCollection Alexanders_theorem.
- Alexanders_theorem wikiPageUsesTemplate Template:Cite_book.
- Alexanders_theorem wikiPageUsesTemplate Template:Cite_journal.
- Alexanders_theorem wikiPageUsesTemplate Template:Knot_theory.
- Alexanders_theorem wikiPageUsesTemplate Template:Knottheory-stub.
- Alexanders_theorem subject Category:Knot_theory.
- Alexanders_theorem comment "In mathematics Alexander's theorem states that every knot or link can be represented as a closed braid. The theorem is named after James Waddell Alexander II, who published its proof in 1923.Braids were first considered as a tool of knot theory by Alexander. His theorem gives a positive answer tois it always possible to transform a given knot into a closed braid?However, the correspondence between knots and braids is clearly not one-to-one: a knot may have many braid representations.".
- Alexanders_theorem label "Alexander's theorem".
- Alexanders_theorem sameAs Satz_von_Alexander.
- Alexanders_theorem sameAs アレクサンダーの定理.
- Alexanders_theorem sameAs m.012z24c8.
- Alexanders_theorem sameAs Q19360789.
- Alexanders_theorem sameAs Q19360789.
- Alexanders_theorem wasDerivedFrom Alexanders_theoremoldid=657240582.
- Alexanders_theorem isPrimaryTopicOf Alexanders_theorem.