A geometric characterization of orient at ion-reversing involutions

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.


Published in:
Journal Of The London Mathematical Society-Second Series, 77, 287-298
Year:
2008
Keywords:
Laboratories:




 Record created 2010-11-30, last modified 2018-03-17


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