About: Andrews–Curtis conjecture

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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.

Attributes	Values
rdf:type	yago:WikicatConjectures yago:Abstraction100002137 yago:Cognition100023271 yago:Concept105835747 yago:Content105809192 yago:Hypothesis105888929 yago:Idea105833840 yago:PsychologicalFeature100023100 yago:Speculation105891783
rdfs:label	Andrews–Curtis conjecture (en) Conjecture d'Andrews-Curtis (fr)
rdfs:comment	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. (en) En mathématiques, la conjecture d'Andrews-Curtis affirme que toute présentation équilibrée du groupe trivial peut être transformée en une présentation triviale par une série de transformations de Nielsen sur les relateurs avec des conjugaisons de relateurs. Il est difficile de réaliser si la conjecture est satisfaite par une présentation équilibrée donnée. (fr)
dct:subject	Conjectures Unsolved problems in mathematics Combinatorial group theory
Wikipage page ID	7754592 (xsd:integer)
Wikipage revision ID	950521000 (xsd:integer)
Link from a Wikipage to another Wikipage	Presentation of a group Nielsen transformation Trivial group Conjectures Unsolved problems in mathematics Proceedings of the American Mathematical Society James J. Andrews (mathematician) Combinatorial group theory Morton L. Curtis Zeeman conjecture Collapsibility
sameAs	Andrews–Curtis conjecture Andrews–Curtis conjecture Andrews–Curtis conjecture Andrews–Curtis conjecture
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Algebra-stub dbt:Citation dbt:Reflist
id	l/l120170 (en)
title	Low-dimensional topology, problems in (en)
has abstract	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. It is known that the Zeeman conjecture on collapsibility implies the Andrews–Curtis conjecture. (en) En mathématiques, la conjecture d'Andrews-Curtis affirme que toute présentation équilibrée du groupe trivial peut être transformée en une présentation triviale par une série de transformations de Nielsen sur les relateurs avec des conjugaisons de relateurs. Il est difficile de réaliser si la conjecture est satisfaite par une présentation équilibrée donnée. Bien qu'il est communément admis que la conjecture de Andrews-Curtis est fausse, il n'existe aucun contre-exemple connu, et il n'existe pas non plus beaucoup de pistes pour trouver de possibles contre-exemples. Il est par contre établi que la conjecture de Zeeman sur la collapsibilité implique la conjecture d'Andrews-Curtis. (fr)
prov:wasDerivedFrom	wikipedia-en:Andrews–Curtis_conjecture?oldid=950521000&ns=0
page length (characters) of wiki page	1552 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Andrews–Curtis_conjecture
is Link from a Wikipage to another Wikipage of	List of conjectures Nielsen transformation James J. Andrews (mathematician) List of African-American inventors and scientists Andrews-Curtis conjecture List of unsolved problems in mathematics Tietze transformations Morton L. Curtis Zeeman conjecture
is Wikipage redirect of	Andrews-Curtis conjecture
is foaf:primaryTopic of	wikipedia-en:Andrews–Curtis_conjecture

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