Seminar on periodic maps by Pierre E. Conner
CP(1) This is the conjugate As we defined it, S cCP(2)~ /=o/ and the restriction /~"/S > CP(1) may be readily identified with - the quotient map /2: S 52 - Thus we have constructed > S/T. an n-fold ramified covering of CP(1) which branches at . 9cal uniformizer~ At each fixed point ~ z~ with respect t__oowhich T(z) = A z . We choose a fixed point Ely - ~ J holomorphic o]. (z)~ defined for Izl < i~ such that 3 a) Rj(O) = b) (Rj(~))n = i + ~, for I~I < 1. ,~ The required uniformizer ~(z) (T,S) there is a is = [t, -Rj(zn),z] Note that I qRj(zn)) n + z n = 1 - 1 - z n + zn = O and We hope t o compute t r a c e (T*I hOwl(s)) finite fixed point set.