Timeline for Does every simplicial polytope have a topology-preserving contractible edge?
Current License: CC BY-SA 3.0
11 events
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| May 5, 2013 at 21:36 | answer | added | Russ Woodroofe | timeline score: 6 | |
| May 2, 2013 at 23:25 | comment | added | Anand Kulkarni | Thanks much, Russ! Indeed, Nevo proves that the link conditions of Dey et al exactly determine contractible edges for all triangulated manifolds, not just 2- and 3-manifolds. That's a start; we need only now ask whether that every polytope has an edge meeting the link conditions. | |
| May 2, 2013 at 17:57 | comment | added | Russ Woodroofe | I'll mention for general interest that Eran Nevo studied edge contractions in his thesis, which is available on the arXiv: arxiv.org/pdf/0709.3265.pdf . He says more about the consequences of an edge contraction than the existence of one, but you might find the algebraic shifting arguments in there interesting. | |
| May 2, 2013 at 6:03 | history | edited | Anand Kulkarni | CC BY-SA 3.0 |
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| May 1, 2013 at 16:34 | comment | added | Anand Kulkarni | I've adjusted this to be more specific. | |
| May 1, 2013 at 16:10 | history | edited | Anand Kulkarni | CC BY-SA 3.0 |
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| May 1, 2013 at 9:46 | comment | added | Fernando Muro | It seems that in your first paragraph you don't really talk about general simplicial complexes but only about triangulations of manifolds. | |
| Apr 30, 2013 at 23:57 | comment | added | Anand Kulkarni | Thanks for pointing this out! I've added language to indicate I'm interested in nontrivial examples: ie, not the simplex. | |
| Apr 30, 2013 at 23:55 | history | edited | Anand Kulkarni | CC BY-SA 3.0 |
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| Apr 30, 2013 at 23:03 | comment | added | Dan Petersen | "On a $d$-simplex, no edge is contractible. [...] Does every simplicial polytope have a contractible edge?". I think you just answered your own question. | |
| Apr 30, 2013 at 22:34 | history | asked | Anand Kulkarni | CC BY-SA 3.0 |