MAXIMUM ORDERS OF PERIODIC MAPS ON CLOSED SURFACES

In this paper, we determine the maximum orders of periodic maps on closed surfaces. For the orientable closed surface of genus g, g greater-than-or-equal-to 2, this maximum order is 4g + 2 (realized by an orientation preserving map) if g is odd and is 4g + 4 (realized by an orientation reversing map) otherwise. For the nonorientable closed surface of genus q, q greater-than-or-equal-to 3, this maximum order is 2q if q is odd and is 2q - 2 otherwise. Furthermore, the maximum order of orientation reversing periodic maps on F(g) is 4g - 4 if g is odd.Mathematics, AppliedMathematicsSCI(E)0ARTICLE3255-2624