Let be the free group generated by and . In this article, we prove that the commutator of and is a product of two squares if and only if is even. We also show using topological methods that there are infinitely many obstructions for an element in to be a product of two squares.
"Commutators and squares in free groups." Algebr. Geom. Topol. 4 (1) 595 - 602, 2004. https://doi.org/10.2140/agt.2004.4.595