Timeline for Structure of Gordian graph of knots
Current License: CC BY-SA 3.0
13 events
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| Dec 31, 2019 at 21:45 | comment | added | Ryan Budney | @AllisonH.Moore: Sorry I missed your comment, Allison. I believe the reference is this: THE GORDIAN COMPLEX OF KNOTS MIKAMI HIRASAWA and YOSHIAKI UCHIDA | |
| Dec 20, 2016 at 18:43 | comment | added | Allison H. Moore | @RyanBudney Do you know where this result about the complete subgraphs comes from? | |
| Nov 21, 2016 at 18:52 | history | edited | Ryan Budney | CC BY-SA 3.0 |
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| Nov 21, 2016 at 18:47 | comment | added | Ryan Budney | @TetsuyaAbe at first glance Nakanishi-Ohyama does not appear to address homogeneity -- it appears to be talking about the Gordian graph decorated with additional information, such as Conway/Jones polynomials. It's unclear to me how to get any purely graph-theoretic information out of this paper. Similarly for the Nakanishi paper, this is the Gordian graph decorated by Alexander invariants. But thanks for letting me know about the papers. I think there are many ways to potentially "decorate" the Gordian graph that are very intuitive that lead to an inhomogeneous object. | |
| Nov 21, 2016 at 9:00 | comment | added | Tetsuya Abe | @ Ryan Budney A (slightly) related papers for homogeneity are projecteuclid.org/download/pdf_1/euclid.hmj/1257544216 and math.kobe-u.ac.jp/HOME/nakanisi/LG2.pdf | |
| Nov 21, 2016 at 8:32 | comment | added | Ryan Budney | @TetsuyaAbe thanks for the update Tetsuya. | |
| Nov 21, 2016 at 8:32 | history | edited | Ryan Budney | CC BY-SA 3.0 |
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| Nov 21, 2016 at 8:26 | comment | added | Tetsuya Abe | @ Misha It is well-known that the Gordian graph of knots is NOT hyperbolic due to Gambaudo an Ghys (2005). smf4.emath.fr/en/Publications/Bulletin/133/pdf/… A closely related paper is the following:projecteuclid.org/euclid.pja/1296570389 | |
| Nov 21, 2016 at 6:06 | history | edited | Ryan Budney | CC BY-SA 3.0 |
some small touch-ups, incorporate Misha's suggestion
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| Nov 20, 2016 at 9:03 | comment | added | Misha | I would add hyperbolicity to this list. | |
| Nov 20, 2016 at 6:28 | comment | added | Sam Nead | The distance to the unknot, in the Gordian graph, is the unknotting number. So we at least know that the Gordian graph has infinite diameter. | |
| Nov 20, 2016 at 6:06 | history | edited | Ryan Budney | CC BY-SA 3.0 |
added 18 characters in body; added 4 characters in body; added 22 characters in body
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| Nov 20, 2016 at 5:50 | history | asked | Ryan Budney | CC BY-SA 3.0 |