Resumen de A geometric characterization of orientation-reversing involutions

Antonio Félix Costa González , Hugo Parlier

• We give a geometric characterization of compact Riemann surfaces admitting orientation�reversing involutions with fixed points. Such surfaces are generally called real surfaces and can be represented by real algebraic curves with non-empty real part. We show that there is a family of disjoint simple closed geodesics that intersect all geodesics of a pants decomposition at least twice in uniquely right angles if and only if such an involution exists. This implies that a surface is real if and only if there is a pants decomposition of the surface with all Fenchel�Nielsen twist parameters equal to 0 or 1/2.