Timeline for Fundamental domain of Möbius transformations
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 5, 2023 at 1:19 | comment | added | Alexandre Eremenko | Some other, more modern books are Maskit, Kleinian groups, and A. Beardon, Geometry of discrete groups. They also contain constructions of fundamental regions. There are two basic constructions: one is called a Ford fundamental region, another Dirichlet fundamental region. | |
| Feb 4, 2023 at 19:49 | comment | added | p6majo | I tried to buy the book by Ford. But I can only find it in the US not shipable to Europe. On the other hand, I found the first 25 pages of the book at googlebooks. Within these 25 pages the isometric circle is discussed, which happens to be exactly the border of the two discs $D_1$ and $D_2$ for the example I showed in the question. Can I generalize this observation, that the fundamental domain is $\mathbb{C}$ with the discs removed that are surrounded by the isometric circles of $a$ and its inverse $a^{-1}$? This would be very neat and simple as well. | |
| Feb 3, 2023 at 0:17 | comment | added | Alexandre Eremenko | For a general construction of fundamental domain (of any properly discontinuous group of linear-fractional transformation) you may consult the book Ford, Automorphic functions, or any other book on Kleinian groups. | |
| Feb 2, 2023 at 19:05 | history | edited | p6majo | CC BY-SA 4.0 |
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| Feb 2, 2023 at 16:56 | review | Close votes | |||
| Feb 8, 2023 at 18:27 | |||||
| Feb 2, 2023 at 16:19 | history | asked | p6majo | CC BY-SA 4.0 |