Sucharit Sarkar
Published 2004-09-06Version 1
Let F_2 be the free group generated by x and y. In this article, we prove that the commutator of x^m and y^n 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 F_2 to be a product of two squares.
Comments: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-27.abs.html
Journal: Algebr. Geom. Topol. 4 (2004) 595-602
Products of Commutators and Products of Squares in a Free Group
Automorphism groups of free groups, surface groups and free abelian groups
Orientable and non-orientable genus $n$ Wicks forms over hyperbolic groups
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