Timeline for What is known about links with a countably-infinite number of tame components?
Current License: CC BY-SA 2.5
8 events
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| Jun 22, 2022 at 7:16 | history | edited | CommunityBot |
replaced http://front.math.ucdavis.edu/ with https://arxiv.org/abs/
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| Feb 1, 2011 at 23:11 | vote | accept | Scott McKuen | ||
| Feb 1, 2011 at 5:37 | comment | added | Scott McKuen | So, a Fraisse link exists and is unique, but two embeddings of it in $\mathbb{R}3$ are not necessarily ambient isotopic, even though there is an ambient isotopy taking any finite portion to its counterpart in the other embedding - and this is simply because a discontinuity could appear in the ambient space in the limit, as the partial isotopies of the chains get pushed to include more and more components? Okay. By the way, the definition you give above for the pro-isotopy relation looks like what model theorists would call a "back-and-forth" argument that two structures are isomorphic. | |
| Jan 31, 2011 at 5:26 | history | edited | Sergey Melikhov | CC BY-SA 2.5 |
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| Jan 31, 2011 at 5:04 | comment | added | Scott McKuen | Yeah, I wasn't totally clear in the first version and should have spelled out the conditions that hold in the Fraïssé limit. I'm not asserting that $L$ and $L'$ are ambient isotopic in cases like your example above. The added bits about the amalgamation property rule out your $L$ as an instance of what I'm looking for. As for the example in your Steenrod Homotopy paper (thanks!) of a sequence of knots $K_1, K_2,...$ where only the adjacent entries link up, I think its set of sublinks satisfies all three conditions above, but the limit object they generate could be a distinct thing entirely. | |
| Jan 31, 2011 at 4:34 | history | edited | Sergey Melikhov | CC BY-SA 2.5 |
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| Jan 31, 2011 at 4:24 | history | edited | Sergey Melikhov | CC BY-SA 2.5 |
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| Jan 31, 2011 at 2:12 | history | answered | Sergey Melikhov | CC BY-SA 2.5 |