Timeline for Singular homology of a graph.
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 16, 2010 at 11:18 | vote | accept | Xandi Tuni | ||
| May 16, 2010 at 11:18 | comment | added | Xandi Tuni | After a first careless check, it appears that Robin and Torsten are right. Summing up that means "yes" for (a) and both parts of (b) and we also have many examples for (z). The answer to (c) is "no way": This kind of singular cohomology behaves very bad for products of graphs. | |
| May 15, 2010 at 11:54 | history | edited | Robin Chapman | CC BY-SA 2.5 |
spelling correction
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| May 15, 2010 at 11:32 | comment | added | Torsten Ekedahl | Indeed this is just the simplicial set associated to the clique simplicial complex of a graph. Any flag complex is (by definition) the clique complex of its 1-skeleton considered as graph. In particular the barycentric subdivision of any simplicial complex is a flag complex and consequently any simplicial complex is homeomorphic to a clique complex. | |
| May 15, 2010 at 11:24 | comment | added | Xandi Tuni | My maps of graphs are not just embeddings (1st paragraph) - the map that sends all of $\Delta_n$ to a single point is a valid morphism. Still: The space $\widehat G$ you suggest is the right candidate for $||G||$ in (a), the inclusion of $|G|$ in $\widehat G$ would yield the sought comparison map. | |
| May 15, 2010 at 11:02 | history | answered | Robin Chapman | CC BY-SA 2.5 |