Timeline for Do all combinatorially distinct fundamental polygons correspond to surfaces?
Current License: CC BY-SA 3.0
12 events
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| Sep 25, 2014 at 2:42 | history | edited | Alexandre Eremenko | CC BY-SA 3.0 |
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| Jun 27, 2014 at 19:43 | comment | added | Joseph O'Rourke | @BenjaminSteinberg: Yes, the definition of fundamental polygon is that each symbol should appear exactly twice. I will make that explicit. Thanks! | |
| Jun 27, 2014 at 17:31 | comment | added | Benjamin Steinberg | To get a surface each letter should appear exactly twice. Maybe this was implicit in the question. | |
| Jun 27, 2014 at 14:20 | comment | added | Benjamin Steinberg | I am confused. There are one-relator groups with even length relations that are not surface groups. The string $ab^6a^{-1}b^{-8}$ defines a non-Hopfian Baumslag-Solitar group and hence is not a surface group. | |
| Jun 27, 2014 at 13:19 | history | edited | Alexandre Eremenko | CC BY-SA 3.0 |
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| Jun 27, 2014 at 13:10 | comment | added | David E Speyer | Also, you need to do orientable and unorientable surfaces separately. | |
| Jun 27, 2014 at 13:09 | comment | added | Alexandre Eremenko | Arnaud, thanks for your correction. | |
| Jun 27, 2014 at 13:08 | history | edited | Alexandre Eremenko | CC BY-SA 3.0 |
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| Jun 27, 2014 at 12:58 | comment | added | Arnaud | Isn't this a proof that the answer to 2. is Yes, i.e. that combinatorially distinct strings can correspond to the same surface ? | |
| Jun 27, 2014 at 12:53 | history | edited | Alexandre Eremenko | CC BY-SA 3.0 |
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| Jun 27, 2014 at 12:47 | vote | accept | Joseph O'Rourke | ||
| Jun 27, 2014 at 12:46 | history | answered | Alexandre Eremenko | CC BY-SA 3.0 |