Timeline for Removing simplices from simplicial complexes without decreasing connectedness
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 16, 2017 at 14:12 | history | edited | Sebastian Goette | CC BY-SA 3.0 |
The original space was not really a simplicial set.
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| Feb 15, 2017 at 21:20 | vote | accept | user1272680 | ||
| Feb 15, 2017 at 21:20 | comment | added | user1272680 | Many thanks for the counterexample, this is really helpful! | |
| Feb 15, 2017 at 20:53 | comment | added | Sebastian Goette | I was just rewriting the answer when your comment showed up. Thanks. | |
| Feb 15, 2017 at 20:53 | comment | added | HJRW | Oh, it looks like you already did this in the edit! | |
| Feb 15, 2017 at 20:52 | history | edited | Sebastian Goette | CC BY-SA 3.0 |
Also works as simplicial complex.
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| Feb 15, 2017 at 20:50 | comment | added | HJRW | This is easy to realize as an ordinary simplicial complex. Take a simplicial circle, and two simplicial discs: one wrapped twice round the circle, one wrapped three times round the circle. As you observe, this is simply connected but non-contractible. Now the removal of any 2-simplex turns the corresponding disc into a homotopy annulus, which again makes the result non-simply connected. | |
| Feb 15, 2017 at 20:16 | history | answered | Sebastian Goette | CC BY-SA 3.0 |