Timeline for How does the topology of the graphs' Riemann surface relate to its knot representation?
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 4, 2020 at 10:29 | comment | added | draks ... | What I want to know: Since the knot construction of bicubic graph deals with orientations at the vertices or between pairs of vertices, Makover's construction of the Riemann Surface of a (bicubic) graph, seems to be based on similar grounds. I wonder about the relation of the knot/link and Riemann surface constructed from the same graph. It looks to me that the knot/link is related to the left-hand turn paths. But what would that mean for the Riemann surface? | |
| Aug 4, 2020 at 10:29 | comment | added | draks ... | @Henry the only choice I make, is how to orient the "fat edges" in the fat/ribbon graph. See also Def. 1 here. | |
| Aug 4, 2020 at 10:01 | comment | added | Henry | The question is not clear to me. It is true that for any planar graph you can associate a knot diagram, using the algorithm you described. But I am not sure what you are asking. | |
| Aug 4, 2020 at 7:54 | comment | added | draks ... | @Sam I edited my question, accordingly... | |
| Aug 4, 2020 at 7:54 | history | edited | draks ... | CC BY-SA 4.0 |
added 10 characters in body
|
| Aug 3, 2020 at 10:48 | comment | added | Sam Nead | Suppose that the initial cubic plane graph has a cycle of odd length. Then the fat graph will not be orientable. So the surface is not a Riemann surface. So, I don't understand the actual question here... | |
| Aug 3, 2020 at 8:39 | history | edited | draks ... | CC BY-SA 4.0 |
added 82 characters in body
|
| Apr 30, 2020 at 22:07 | comment | added | draks ... | @j.c. I removed the rank computation, but I'm not able to choose a specific construction of a Riemann surface... | |
| Apr 30, 2020 at 21:37 | history | edited | draks ... | CC BY-SA 4.0 |
deleted 35 characters in body
|
| S May 25, 2018 at 15:04 | history | bounty ended | CommunityBot | ||
| S May 25, 2018 at 15:04 | history | notice removed | CommunityBot | ||
| May 18, 2018 at 12:08 | history | edited | draks ... | CC BY-SA 4.0 |
added 293 characters in body
|
| May 17, 2018 at 14:52 | comment | added | j.c. | The computation of the rank and Ihara zeta function for this graph seem to be irrelevant to the actual question. I recommend editing that out and adding a self-contained description of the construction of a Riemann surface that you have in mind. | |
| S May 17, 2018 at 13:43 | history | bounty started | draks ... | ||
| S May 17, 2018 at 13:43 | history | notice added | draks ... | Draw attention | |
| Jul 10, 2017 at 13:59 | history | asked | draks ... | CC BY-SA 3.0 |