We show that the equation associated with a group word can be solved over a hyperlinear group if its content — that is, its augmentation in — does not lie in the second term of the lower central series of . Moreover, if is finite, then a solution can be found in a finite extension of . The method of proof extends techniques developed by Gerstenhaber and Rothaus, and uses computations in –local homotopy theory and cohomology of compact Lie groups.
"New topological methods to solve equations over groups." Algebr. Geom. Topol. 17 (1) 331 - 353, 2017. https://doi.org/10.2140/agt.2017.17.331