Timeline for Minimal set of geometric moves in various equivalence classes of triangulated geometries
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| Aug 16, 2023 at 11:49 | comment | added | Kregnach | @SamNead the paper you suggested is really great and useful, thank you! | |
| Aug 16, 2023 at 11:11 | history | edited | Kregnach | CC BY-SA 4.0 |
changed links to dual-edges, and external links to half-dual-edges
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| Aug 16, 2023 at 11:04 | comment | added | Kregnach | @Sam Nead , sorry, I need to get used to the proper jargon. In my group, we used to call edges links, as we didn't really care about the precise mathematical definitions but just wanted to use the fact, that a "link" as its name suggests, links two vertices. Now that I need to think about mathematical properties (like those in my previous questions), and as I'm asking mathematicians, I need to be more precise. | |
| Aug 16, 2023 at 10:28 | comment | added | Sam Nead | Goodness. And I suppose that an "external legs" is a half-edge. I don't know what an "unclosed leg" is. | |
| Aug 16, 2023 at 10:25 | comment | added | Sam Nead | Why do you call so many things "links"? Where is that language coming from? | |
| Aug 16, 2023 at 10:24 | comment | added | Sam Nead | A face in the dual graph (dual to an edge in the primal) could be called a "dual face". | |
| Aug 16, 2023 at 10:24 | comment | added | Sam Nead | Finally, this paper (arxiv.org/abs/1812.02806) gives work in the direction you desire. If it does not answer your question, then you might reach out to the mathematicians mentioned in the abstract. | |
| Aug 16, 2023 at 10:22 | comment | added | Kregnach | I just meant a connection between two nodes of the dual graph (thus faces of the original triangulations), I got to know that the connection between vertices is "edges", but I don't know how to call the faces in the dual graph, so I called them links. Correct me if I'm wrong please. | |
| Aug 16, 2023 at 10:19 | comment | added | Sam Nead | (I make this suggestion because "link" means something completely different in the context of combinatorial topology.) | |
| Aug 16, 2023 at 10:18 | comment | added | Sam Nead | You use "link" where I would write "edge" and you use "node" where I would write "vertex". If you want to distinguish objects in the dual from objects in the primal (that is, original) then add the adjective "dual". As in - "in the dual graph, all dual vertices have degree four" or "we require that dual edges meet two distinct dual vertices" and so on. | |
| Aug 16, 2023 at 6:51 | comment | added | Kregnach | I considered doing so, just didn't know who to ask among many people, thank you for your recommendation! | |
| Aug 16, 2023 at 6:35 | comment | added | Ryan Budney | @Kregnach: You should try sending your question via email to Jaco and Rubinstein. They likely have thoughts on most of your questions. | |
| Aug 16, 2023 at 5:33 | comment | added | Kregnach | I'm interested in specific moves for different manifold constraints (case A case B), as the minimal set of moves. In general Pachner are moves, which leave a boundary of a subset of a triangulation unchanged , while changing the interior. I gave examples of that specifically for different manifold constraints. I would be interested in a sequence of moves that reaches the configuration I specified from the initial one, without involving the particular move that directly brings that there. If it's possible, then that move is not "elementary" but composite, thus not part of the minimal set. | |
| Aug 16, 2023 at 1:51 | comment | added | Ryan Budney | Pachner moves are the answer to your concern in your first paragraph. But do you mean something more specific when you ask for a "minimal" set? Minimal in what sense? | |
| Aug 15, 2023 at 19:43 | history | edited | Kregnach | CC BY-SA 4.0 |
Spelling correction
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| Aug 15, 2023 at 19:42 | comment | added | Kregnach | Unfortunately I don't understand the paper (entirely). I'm not too familiar with abstract math, and it's hard for me to read it. I cannot find answer to my question in this paper. | |
| Aug 15, 2023 at 17:39 | comment | added | Gael Meigniez | What about Pachner moves? Pachner, Udo (1991), "P.L. homeomorphic manifolds are equivalent by elementary shellings", European Journal of Combinatorics, 12 (2): 129–145, doi:10.1016/s0195-6698(13)80080-7 | |
| Aug 15, 2023 at 15:35 | history | edited | Kregnach | CC BY-SA 4.0 |
Finished an unfinished sentence in Case B.
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| Aug 15, 2023 at 15:21 | history | asked | Kregnach | CC BY-SA 4.0 |