Andrews-Curtis conjecture

From Wikipedia, the free encyclopedia

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, (Andrews & Curtis 1965). It is difficult to verify whether the conjecture holds for a given balanced presentation or not.

Although it is believed that the Andrews-Curtis conjecture is false, there are no counter-examples known, nor are there many good ideas for possible counter-examples.

[edit] References

This article needs additional citations for verification. Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (January 2008)

• Andrews, J. J. & Curtis, M. L. (1965), “Free groups and handlebodies”, Proceedings of the American Mathematical Society 16: 192–195, MR0173241, ISSN 0002-9939, DOI 10.2307/2033843