Matches in DBpedia 2015-10 for { ?s ?p "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."@en }
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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.".