On the topological type of anticonformal square roots of automorphisms of Riemann surfaces

Let X be a compact Riemann surface and f be a conformal automorphism of X of order n. An anticonformal square root of f is an anticonformal automorphism g of X such that g(2) = f. If g(1) and g(2) are two anticonformal square roots of f we study the problem of whether g(1) and g(2) have the same topological type, i. e., if there exists a homeomorphism h:X-->X such that g(1) = hg(2)h(-1). We use techniques of noneuclidean crystallographic (NEC) groups and the topological classification of orientation reversing maps of finite period on surfaces given in [C1] and [Y].