Galois theory manifolds K-theory rational maps Einstein Chair mapping class groups circle homeomorphisms Douady--Earle extension laminations earthquakes monodromy spaces of polynomials absolute cyclotomy quantized calculus quasiconformal mappings Hauptvermutung singularities incompressible fluids rational homotopy theory moduli spaces decorated Teichmüller space Whitehead Nightmare string topology solenoid Sullivan dictionary Bowen-Series maps Sullivan models