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Sep 19, 2020 at 20:50 comment added coudy Yes, indeed. Corrected.
Sep 19, 2020 at 20:49 history edited coudy CC BY-SA 4.0
typo
Sep 19, 2020 at 16:46 comment added Amirhossein @coudy Thank you, but I think you mean the book "Geometry and Spectra of Compact Riemann Surfaces". Am I correct?
Sep 16, 2020 at 20:10 history edited coudy CC BY-SA 4.0
better picture
Sep 16, 2020 at 20:06 comment added coudy Yes indeed this is a quick sketch. I edited the picture a bit. The fundamental domain includes the three funnels as you said.
Sep 16, 2020 at 20:05 history edited coudy CC BY-SA 4.0
better picture
Sep 16, 2020 at 19:49 comment added Sebastian Goette Very nice explanation, but the picture is a bit sloppy. If someone unfamiliar with hyperbolic geometry sees it, they might get wrong ideas. For example, two geodesics perpendicular to the geodesic $\beta_1$ cannot have a common endpoint at infinity unless they are equal. The shaded area seems to be a fundamental domain for the pair of pants with ends attached to them (like a "pair of flares", to stay in jargon).
Sep 16, 2020 at 15:43 history answered coudy CC BY-SA 4.0