Timeline for Complement to a union of spheres in a sphere
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 20, 2021 at 10:45 | vote | accept | iou | ||
| Jan 19, 2021 at 21:15 | history | became hot network question | |||
| Jan 19, 2021 at 17:10 | answer | added | Tyler Lawson | timeline score: 3 | |
| S Jan 19, 2021 at 16:13 | history | suggested | Samuel Lelièvre | CC BY-SA 4.0 |
Rephrase as complement to a union of spheres rather than to a set of spheres
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| Jan 19, 2021 at 14:48 | comment | added | Connor Malin | Alexander duality for manifolds can be refined to a statement about the Thom space of the normal bundle being stably equivalent to the complement of $X$ and a disjoint basepoint in the sphere. In fact, the stabilization need only happen once, and in your setting the stabilization has already happened since we can imagine these all embedded in a codimension 2 equator. The addition of the embeddings being uninteresting implies the normal bundles are trivial, so up to removing another point, yes the homotopy type is a wedge of spheres, probably not difficult to answer the rest from there. | |
| Jan 19, 2021 at 14:44 | answer | added | Danny Ruberman | timeline score: 3 | |
| Jan 19, 2021 at 14:06 | comment | added | iou | @ThomasRot Right. But I'm interested in a homotopy type of a complement rather than in homology itself. Is my suggestion about a homotopy type correct? Is it a wedge of spheres? | |
| Jan 19, 2021 at 14:04 | review | Suggested edits | |||
| S Jan 19, 2021 at 16:13 | |||||
| Jan 19, 2021 at 14:04 | comment | added | Thomas Rot | Alexander duality (en.wikipedia.org/wiki/Alexander_duality) is probably the easiest way of computing the homology of the complement. | |
| Jan 19, 2021 at 13:12 | history | asked | iou | CC BY-SA 4.0 |