Timeline for Vietoris-Rips complex homology of a higher degree than the ambient dimension
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jun 18, 2018 at 8:40 | comment | added | Arkadi | Also note, that the example by Barratt and Milnor uses a countable wedge of spheres, whereas I tried to keep it simpler by considering only finite complexes. | |
| Jun 18, 2018 at 8:28 | comment | added | Arkadi | Thanks for that insightful answer. I leave the answer unaccepted, though, to hope someone might have an idea about Euclidean distances or $d>2$. | |
| Jun 14, 2018 at 19:58 | history | edited | j.c. | CC BY-SA 4.0 |
fix per Luc Guyot's comment.
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| Jun 14, 2018 at 19:39 | comment | added | j.c. | @LucGuyot You're right of course. I will edit... | |
| Jun 14, 2018 at 19:26 | comment | added | Luc Guyot | About "The Vietoris-Rips complex at scale $\epsilon$ for a point set $X$ in $\mathbb{R}^d$ coincides with the Čech complex for a set of balls of radius $\epsilon/2$ centered at the points of $X$." This holds only for the points and edges of the two complexes in general. If the distance is $\ell_{\infty}$, the two complexes coincide. | |
| Jun 14, 2018 at 17:45 | comment | added | j.c. | Ian Agol updated the link in his answer to a revised version of Zastrow's paper available here: mat.ug.edu.pl/~zastrow/Nnonano.htm | |
| Jun 14, 2018 at 16:41 | history | answered | j.c. | CC BY-SA 4.0 |