Timeline for Minimal area of non-planar lattice curves
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4 events
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| May 8, 2014 at 15:38 | comment | added | Martin Tancer | Yes, it works in higher dimensions as well. I did not emphasize it, but the proof is written for arbirtrary $d \geq 3$. I am not sure what you exactly mean with hypertoroidal lattice. But if I guess well, the contractibility of curves is not important. It is more important whether you can have a nontrivial $2$-cycle ($S$ in the answer) such that it has an odd number of squares. It seems to me to be possible in some hypertoroidal lattices of some appropriate dimensions such as $3 \times 3 \times 3$. | |
| May 8, 2014 at 15:15 | comment | added | FreeQuark | Thank you for your answer! I am not too familiar with homological algebra, but I understood your argument. Does it extend to higher dimensions, $d=4$ in particular? And for hypertoroidal lattices I think your argument would be valid for the set of contractible lattice curves too, wouldn't it? | |
| May 4, 2014 at 16:20 | history | edited | Martin Tancer | CC BY-SA 3.0 |
Added a suggestion how to
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| May 4, 2014 at 15:56 | history | answered | Martin Tancer | CC BY-SA 3.0 |