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research article
A geometric characterization of orient at ion-reversing involutions
Costa, Antonio F.
•
Parlier, Hugo
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.
Type
research article
Web of Science ID
WOS:000255084400002
Authors
Costa, Antonio F.
•
Parlier, Hugo
Publication date
2008
Volume
77
Start page
287
End page
298
Subjects
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
November 30, 2010
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