In mathematics, the Andrews–Curtis conjecture states that every balanced presentation of the trivial group can be transformed into a trivial presentation by a sequence of Nielsen transformations on the relators together with conjugations of relators, named after James J. Andrews and Morton L. Curtis who proposed it in 1965. It is difficult to verify whether the conjecture holds for a given balanced presentation or not.
It is widely believed that the Andrews–Curtis conjecture is false. While there are no counterexamples known, there are numerous potential counterexamples.[1] It is known that the Zeeman conjecture on collapsibility implies the Andrews–Curtis conjecture.[2]
andrews, curtis, conjecture, mathematics, states, that, every, balanced, presentation, trivial, group, transformed, into, trivial, presentation, sequence, nielsen, transformations, relators, together, with, conjugations, relators, named, after, james, andrews,. In mathematics the Andrews Curtis conjecture states that every balanced presentation of the trivial group can be transformed into a trivial presentation by a sequence of Nielsen transformations on the relators together with conjugations of relators named after James J Andrews and Morton L Curtis who proposed it in 1965 It is difficult to verify whether the conjecture holds for a given balanced presentation or not It is widely believed that the Andrews Curtis conjecture is false While there are no counterexamples known there are numerous potential counterexamples 1 It is known that the Zeeman conjecture on collapsibility implies the Andrews Curtis conjecture 2 References EditAndrews J J Curtis M L 1965 Free groups and handlebodies Proceedings of the American Mathematical Society American Mathematical Society 16 2 192 195 doi 10 2307 2033843 JSTOR 2033843 MR 0173241 Low dimensional topology problems in Encyclopedia of Mathematics EMS Press 2001 1994 Open problems in combinatorial group theory Collapsibility Encyclopedia of Mathematics EMS Press 2001 1994 This algebra related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Andrews Curtis conjecture amp oldid 950521000, wikipedia, wiki, book, books, library,
