Timeline for Bing sling isotopy to unknot
Current License: CC BY-SA 4.0
18 events
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| Dec 28, 2022 at 7:12 | history | edited | amd1234 | CC BY-SA 4.0 |
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| Dec 27, 2022 at 19:03 | answer | added | amd1234 | timeline score: 0 | |
| Dec 26, 2022 at 9:35 | answer | added | Shijie Gu | timeline score: 6 | |
| Dec 24, 2022 at 8:53 | history | edited | amd1234 | CC BY-SA 4.0 |
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| Dec 23, 2022 at 22:00 | history | edited | YCor | CC BY-SA 4.0 |
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| Dec 23, 2022 at 20:07 | comment | added | amd1234 | @RyanBudney Yes this precisely what i write (sorry if its not clear - i'll edit the question). The Bing Sling is such an example. However it is interesting to see Gillman's example too since this knot fails to pierce a disc at each point but is still isotopic to the unknot | |
| Dec 23, 2022 at 20:07 | history | edited | LSpice | CC BY-SA 4.0 |
More information about links; consistent capitalisation of "Bing sling"
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| Dec 23, 2022 at 20:05 | history | edited | amd1234 | CC BY-SA 4.0 |
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| Dec 23, 2022 at 19:59 | history | edited | amd1234 | CC BY-SA 4.0 |
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| Dec 23, 2022 at 18:45 | review | Close votes | |||
| Dec 28, 2022 at 3:06 | |||||
| Dec 23, 2022 at 18:33 | comment | added | Ryan Budney | I suppose the problematic knots are the ones without a single tame point. | |
| Dec 23, 2022 at 18:26 | comment | added | Ryan Budney | I voted to close as the question is lacking details. Presumably the context is what might be called "weak" topological isotopy of embeddings, we are asking if the space of all topological embeddings Emb(S^1, R^3) with the compact-open topology is connected. The Alexander trick provides for this, when the knot is tame, so the issue is the non-tame knots. You should probably change the title, as well, as I imagine Rolfsen has asked more than one question in his career. | |
| Dec 23, 2022 at 17:40 | comment | added | PseudoNeo | In other words, the thing knot theory prevents you from doing is pulling on the ends of the string to make the knot smaller and smaller. The kind of things you do in real life when you tie a knot, you see? | |
| Dec 23, 2022 at 16:51 | comment | added | HJRW | @ConnorMalin: Thanks for the reminder! | |
| Dec 23, 2022 at 16:43 | comment | added | Connor Malin | @HJRW Here topologically isotopic means that there is a path of topological embeddings from one knot to another. For tame knots, there is always a path to the unknot which is done by first isolating the ''interesting'' stuff into an $\epsilon$-ball, then limiting it to a point (in a way that preserves injectivity). What most people call knot theory is the study of smooth embeddings up to smooth isotopy which avoids this trickery. | |
| Dec 23, 2022 at 15:47 | comment | added | HJRW | Can you clarify Rolfsen’s question? It seems like there’s a missing hypothesis. Obviously there are knots that aren’t isotopic to the unknot. | |
| Dec 23, 2022 at 8:45 | history | edited | amd1234 | CC BY-SA 4.0 |
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| Dec 23, 2022 at 7:59 | history | asked | amd1234 | CC BY-SA 4.0 |