Algebraic & Geometric Topology 4 (2004) 595–602

DOI: 10.2140/agt.2004.4.595

Abstract

Let F₂ be the free group generated by x and y. In this article, we prove that the commutator of x^m and yⁿ is a product of two squares if and only if mn is even. We also show using topological methods that there are infinitely many obstructions for an element in F₂ to be a product of two squares.

Keywords

Commutators, free groups, products of commutators

Mathematical Subject Classification

Primary: 20F12

Secondary: 57M07

References

Publication

Received: 2 January 2003
Revised: 25 March 2004
Accepted: 12 July 2004
Published: 5 November 2004

Authors