Timeline for Framed singular knots
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 18, 2015 at 1:07 | comment | added | Dylan Thurston | I don't quite know what you mean by "the angle between the frames", but something like that should be what I meant. | |
| Jun 17, 2015 at 15:15 | comment | added | Paul | @Dylan maybe something like this corrects for your comment: The image of $S^{1}\times\{0\}\times\{1\}$ provides a framing. So we further require that at each double point of $f$, the angle between the frames of the two strands to be $\pi$. | |
| Jun 17, 2015 at 14:54 | comment | added | Paul | @Dylan hmmm I certainly don't want the framing to pass through the singularities in S^3. Could you say a bit more about what the standard framing of a singular knot is, or provide a reference? | |
| Jun 17, 2015 at 10:54 | comment | added | Dylan Thurston | I don't think this is standard. The Reidemeister moves will be easy to work out, of course. You may find it easier to work with PL knots (as Reidemeister did), rather than working through the singularity theory. | |
| Jun 17, 2015 at 10:53 | comment | added | Dylan Thurston | The framings you are considering are not the standard framings on singular knots. Typically, you would pin down the framings at the singularities, looking at something more like an embedding of a ribbon with 4-valent vertices. In your framings, a "twist" is allowed to pass through a singularity, so there is only $\mathbb{Z}$ worth of framings for a given unframed singular knot. | |
| Jun 17, 2015 at 5:00 | history | edited | Paul | CC BY-SA 3.0 |
Restricted function to S1 in the list of conditions
|
| Jun 16, 2015 at 18:01 | history | asked | Paul | CC BY-SA 3.0 |