Mathematics – Complex Variables
Scientific paper
2005-01-21
Mathematics
Complex Variables
43 pages 11 figures to appear Geometria Dedicata
Scientific paper
For two generator free Fuchsian groups, the quotient three manifold is a genus two solid handlebody and its boundary is a hyperelliptic Riemann surface. The convex core is also a hyperelliptic Riemann surface. We find the Weierstrass points of both of these surfaces. We then generalize the notion of a hyperelliptic Riemann surface to a ``hyperelliptic'' three manifold. We show that the handlebody has a unique order two isometry fixing six unique geodesic line segments, which we call the {\sl Weierstrass lines} of the handlebody. The Weierstrass lines are, of course, the analogue of the Weierstrass points on the boundary surface. Further, we show that the manifold is foliated by surfaces equidistant from the convex core, each fixed by the isometry of order two. The restriction of this involution to the equidistant surface fixes six {\sl generalized Weierstrass points} on the surface.
Gilman Jane
Keen Linda
No associations
LandOfFree
The Geometry of Two Generator Groups: Hyperelliptic Handlebodies does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Geometry of Two Generator Groups: Hyperelliptic Handlebodies, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Geometry of Two Generator Groups: Hyperelliptic Handlebodies will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-593912