Timeline for simplicial complex of two covers
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 26, 2020 at 16:02 | comment | added | Edwin Beggs | It is because the empty set is not allowed in a multi-index $(\alpha,\pi)$. This likely means that we have a quotient of a simplical complex, not a simplical complex... | |
| Mar 26, 2020 at 12:21 | comment | added | Henry Adams | I don't yet understand the definition of (2) then. The vertices in (2) are all pairs $(a,\pi)$ where $U_a\cap V_\pi\neq\emptyset$. What do you mean when you say that $\{\{a,b,c\},\{1,2\}\}$ could be a simplex of (2) --- what are the vertices in this simplex? Are the vertices of $\{\{a,b,c\},\{1,2\}\}$ given by $(a,1), (a,2), (b,1), (b,2), (c,1), (c,2)$? | |
| Mar 26, 2020 at 12:13 | history | edited | Henry Adams | CC BY-SA 4.0 |
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| Mar 26, 2020 at 7:42 | comment | added | Edwin Beggs | The comment about (1) is correct. For (2) it is not the same as there $U_a$ itself would be a vertex, but this is not allowed under (2). The vertices are the same as (1) but the higher dimensions are reduced. | |
| Mar 25, 2020 at 2:55 | history | answered | Henry Adams | CC BY-SA 4.0 |