Alan Logan

Examples of Makanin-Razborov diagrams

Makanin-Razborov diagrams are a way of understanding the solutions to equations in free groups. There exists an algorithm to compute these diagrams, but this algorithm is of triply-exponential complexity! We give concrete examples of Makanin-Razborov diagrams corresponding to equations of the form W(x, y)=U(a, b), and provide an effective procedure to compute these diagrams. Our key innovation is to view solutions to such equations are homomorphisms between two-generator, one-relator groups with torsion.