11. Equivalently, it is a manifold that is ( if connected ) monodromy acting by affine transformations. 12. A change of basepoint merely results in a ( simultaneous ) conjugation of all the monodromy matrices. 13. In particular, many of these self-similar groups arise as iterated monodromy groups of complex polynomials. 14. However, if the monodromy is nontrivial, there is no such gauge transformation for the whole outside region. 15. Iterated monodromy groups of rational functions usually have exotic properties from the point of view of classical group theory. 16. This is called the "'monodromy theorem "'and its statement is made precise below. 17. The proof of the existence of such differential equations by previously known monodromy matrices is one of the Hilbert problems. 18. This Chekanov-Eliashberg invariant yields an invariant for loops of Legendrian knots by considering the monodromy of the loops. 19. The monodromy matrices modulo simultaneous conjugation define the "'monodromy data "'of the Fuchsian system. 20. The monodromy matrices modulo simultaneous conjugation define the "'monodromy data "'of the Fuchsian system.
