Memoirs of the American Mathematical Society 2007; 156 pp; softcover Volume: 186 ISBN10: 0821839454 ISBN13: 9780821839454 List Price: US$72 Individual Members: US$43.20 Institutional Members: US$57.60 Order Code: MEMO/186/873
 Exponential equations in free groups were studied initially by Lyndon and Schützenberger and then by Comerford and Edmunds. Comerford and Edmunds showed that the problem of determining whether or not the class of quadratic exponential equations have solution is decidable, in finitely generated free groups. In this paper the author shows that for finite systems of quadratic exponential equations decidability passes, under certain hypotheses, from the factor groups to free products and onerelator products. Table of Contents  Introduction
 Quadratic words
 Quadratic exponential equations and \({\mathcal L}\)genus
 Resolutions of quadratic equations
 Decision problems
 Pictures
 Corridors
 Angle assignment
 Curvature
 Configurations \(C\)
 Configurations \(D\)
 Final angle adjustment
 Isoperimetry
 Proof of Theorem 5.9
 Bibliography
