Timeline for On a Robin Forman's remark on combinatorial simplicial complexes
Current License: CC BY-SA 3.0
7 events
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| Nov 29, 2017 at 16:58 | comment | added | Gjergji Zaimi | (This way of phrasing the proof was not in Lovasz's original paper, but you can read it in chapter 2 of "A course in Topological combinatorics" by Mark de Longueville) | |
| Nov 29, 2017 at 16:57 | comment | added | Gjergji Zaimi | Lovasz initiated a whole field of determining chromatic properties of graphs from the topological properties of its neighorhood complex or various hom complexes. For the original example of the Kneser graph $K_{n,k}$, Lovasz needed to compute the connectivity of its neghborhood complex, but this ends up being homotopy equivalent to a wedge of spheres of dimensions $n-2k$, so the connectivity is exactly $n-2k-1$ and in turn the chromatic number is exactly $n-2k+2$. | |
| Nov 28, 2017 at 2:56 | comment | added | Vidit Nanda | Here's a compelling list. I particularly like Bjorner's paper called "a cell complex in number theory". google.com/… | |
| Nov 27, 2017 at 23:45 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Spelling of "neophyte."
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| Nov 27, 2017 at 23:41 | comment | added | Joseph O'Rourke | I am not sure this qualifies as a "practical example," but shellable simplicial complexes are wedges of spheres of equal dimension. Björner & Wachs generalized to non-pure wedges of spheres (not all equal dimensions), partly to address questions in arrangements of subspaces. "Shellable nonpure complexes and posets. I." Transactions AMS 348.4 (1996): 1299-1327. | |
| Nov 27, 2017 at 23:11 | comment | added | darij grinberg | You get a lot of alternating-sum identities out of it, at least :) | |
| Nov 27, 2017 at 21:36 | history | asked | Mikhail Tikhomirov | CC BY-SA 3.0 |