Timeline for Visualising locally flat embeddings of surfaces in R^4
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 16, 2013 at 17:46 | answer | added | Scott Carter | timeline score: 3 | |
| Dec 5, 2012 at 6:12 | comment | added | Greg Friedman | Coming at this with a lot of ignorance, this raises the following related question: are there locally-flat embeddings of surfaces in $\mathbb R^4$ that are not smoothable embeddings but such that the intersection with every hyperplane parallel to a given one are all sufficiently "nice" (either smoothly embedded curves, smoothly immersed curves, or finite sets of points (or unions of such things))? | |
| Nov 29, 2012 at 15:49 | comment | added | aglearner | Paul I understand that some of intersections of the surface with linear subspaces can be smooth, as in you example. I wonder if one can tell what would be the worst possible intersection for your example. How would it look like? | |
| Nov 28, 2012 at 15:54 | comment | added | Paul | Not quite what you want, but if you take a knot in $R^3$ which is topologically slice but not slice, e.g. the whitehead double of the trefoil, it bounds a locally flat continuously embedded disk in upper half-$R^4$, but does not bound a smooth such disk. So the intersection of this weird disk with a linear hyperplane is a smooth knot. | |
| Nov 23, 2012 at 20:35 | history | asked | aglearner | CC BY-SA 3.0 |