Timeline for Which knot invariants have no known diagram-independent descriptions?
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| S Oct 23, 2019 at 5:01 | history | bounty ended | CommunityBot | ||
| S Oct 23, 2019 at 5:01 | history | notice removed | CommunityBot | ||
| Oct 19, 2019 at 12:56 | history | edited | Keshav Srinivasan | CC BY-SA 4.0 |
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| Oct 16, 2019 at 3:33 | comment | added | Ryan Budney | @Keshav, I'll leave it up to you to decide if that's in the spirit of your question. | |
| Oct 15, 2019 at 23:41 | comment | added | Keshav Srinivasan | @RyanBudney Can’t you just say “The crossing number of a diagram D is the minimum of the number of crossings of all diagrams which can be obtained from D by a sequence of Reidemeister moves”? And surely that is invariant under Reidemeister moves. | |
| Oct 15, 2019 at 16:47 | comment | added | Ryan Budney | @Marc: I would say the minimal crossing number is not a diagram-defined invariant as described in the question. You would need to be able to compute it from any diagram of the knot, and show this number does not change under Reidemeister moves. I don't believe anyone has this approach to crossing number. | |
| Oct 15, 2019 at 15:15 | comment | added | Keshav Srinivasan | @RyanBudney I changed most to many. I think “most found in the past few decades” would probably be accurate. | |
| Oct 15, 2019 at 15:13 | history | edited | Keshav Srinivasan | CC BY-SA 4.0 |
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| Oct 15, 2019 at 14:10 | comment | added | Marc Kegel | Is there a way to understand the minimal crossing number of a knot without using diagrams? | |
| Oct 15, 2019 at 9:03 | answer | added | Adrien | timeline score: 8 | |
| Oct 15, 2019 at 6:24 | comment | added | Ryan Budney | I would maybe disagree with your central assertion. How are you counting "knot invariants"? Many knot invariants have no known (reasonable) diagrammatic formulation. | |
| S Oct 15, 2019 at 3:15 | history | bounty started | Keshav Srinivasan | ||
| S Oct 15, 2019 at 3:15 | history | notice added | Keshav Srinivasan | Draw attention | |
| Sep 11, 2019 at 12:36 | comment | added | Marco Golla | @Wojowu: tri-colorings correspond to (certain) representations of the fundamental group of the knot complement into $S_3$. More generally, $p$-colorings correspond to (certain) representations into the dihedral group with $2p$ elements. | |
| Sep 11, 2019 at 12:02 | comment | added | Danny Ruberman | Many knot invariants such as the volume (and other hyperbolic invariants) or invariants coming from gauge theory are not described (and certainly were not discovered) in the diagrammatic way you suggest. It might be better to ask which diagrammatic invariants (do or) do not have known diagram-independent descriptions. | |
| Sep 11, 2019 at 10:30 | comment | added | Wojowu | Does tricolorability have such a description? | |
| Sep 11, 2019 at 7:54 | history | asked | Keshav Srinivasan | CC BY-SA 4.0 |