Timeline for Is Euler characteristic of a simplicial complex upper bounded by a polynomial in the number of its facets ?
Current License: CC BY-SA 3.0
6 events
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| May 16, 2012 at 0:00 | comment | added | Patricia Hersh | Hi David! Right now, I can only prove your conjecture for "sufficiently large number of vertices", where "sufficiently large" depends heavily on $d$. I then wondered about proving your conjecture by induction on $d$, using Mayer-Vietorus and a facet ordering to try to bound the total increase in Betti numbers under the various facet attachments. No luck yet. Just in case you are interested in the above paper, it's best to get it at www4.ncsu.edu/~plhersh/papers.html because unfortunately there was a small mistake in the published version that was only caught and corrected later. | |
| May 15, 2012 at 16:23 | comment | added | Patricia Hersh | I haven't thought about it yet. Will do so soon. | |
| May 15, 2012 at 16:22 | history | edited | Patricia Hersh | CC BY-SA 3.0 |
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| May 15, 2012 at 16:20 | comment | added | David E Speyer | Hi Tricia! Any idea whether it might be true that a simplicial conplex with $v$ vertices and $f$ facets has Euler characteristic (or, more strongly, total Betti number) $e^{O(\log v \log f)}$? | |
| May 15, 2012 at 15:55 | history | edited | Patricia Hersh | CC BY-SA 3.0 |
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| May 15, 2012 at 15:22 | history | answered | Patricia Hersh | CC BY-SA 3.0 |