Timeline for The simplicial set with a unique non-degenerate simplex in each dimension
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 5, 2023 at 10:51 | vote | accept | user494312 | ||
| Jan 31, 2023 at 20:29 | comment | added | Dmitri Pavlov | @user494312: As already pointed out in the comments, the claim about truncated simplicial sets is only true in odd dimensions. You can easily prove this using the technique explained in the answer, applying it to the map from S to the simplicial n-sphere. | |
| Jan 31, 2023 at 11:44 | comment | added | IJL | In odd dimensions you get up to homotopy a sphere and in even dimensions you get something contractible. | |
| Jan 31, 2023 at 10:09 | comment | added | Zhen Lin | I don't think so. As was suggested to you, for $N = 2$ you get the topologist's dunce hat. | |
| Jan 31, 2023 at 9:51 | comment | added | user494312 | If we restrict the dimension, we get a simplicial sphere, right ? Namely, the following property describes a simplicial sphere: "in each dimension <N there is a unique non-degenerate simplex, and, moreover, all its faces are non-degenerate; in each dimension $\geq N$ each simplex is degenerate". | |
| Jan 31, 2023 at 9:48 | comment | added | user494312 | In fact, I am interested in the set $S$ itself. If one requires the stronger property suggested by Zhen Lin "in each dimension there is a unique non-degenerate simplex, and, moreover, all its faces are non-degenerate', it does seem to describe a simplicial set uniquely. | |
| Jan 31, 2023 at 8:35 | history | answered | Dmitri Pavlov | CC BY-SA 4.0 |