Timeline for Abelian covering of link complement
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 26, 2023 at 18:26 | answer | added | Dave Davidson | timeline score: 0 | |
| Mar 16, 2023 at 23:55 | answer | added | Sam Nead | timeline score: 1 | |
| Mar 16, 2023 at 12:21 | history | edited | LSpice | CC BY-SA 4.0 |
'compliment' -> 'complement'; `\backslash` -> `\setminus`
|
| S Mar 16, 2023 at 12:17 | history | suggested | Дина Чет | CC BY-SA 4.0 |
'covering' instead of 'universal covering'
|
| Mar 16, 2023 at 11:22 | comment | added | Glorfindel | Welcome to MathOverflow! Please use the Contact Us form to have your accounts merged, to regain full control over your posts. | |
| Mar 16, 2023 at 10:31 | review | Suggested edits | |||
| S Mar 16, 2023 at 12:17 | |||||
| Mar 16, 2023 at 9:44 | comment | added | HJRW | To expand on Sam Nead's question: the "universal abelian cover" of a manifold $M$ usually means the covering space corresponding to the kernel of the Hurewicz map $\pi_1(M)\to H_1(M,\mathbb{Z})$. In the case of a link complement, this covering spaces never has finite index (because $H_1(M,\mathbb{Z})$ is infinite). So the words "finite index" make the question unclear. Assuming you just want to delete the words "finite index", many tools are available, as the other comments have indicated. But please edit to clarify! | |
| Mar 16, 2023 at 3:46 | review | Close votes | |||
| Mar 21, 2023 at 3:04 | |||||
| Mar 16, 2023 at 3:31 | comment | added | Ryan Budney | The homology of abelian covers of link exteriors, and of branched covers of links in spheres were two of the first invariants ever considered, in the beginning of knot theory. So yes we can compute these things. Some have taught computers to do it for us. | |
| Mar 16, 2023 at 0:28 | comment | added | gdd | For the fundamental group of a link complement, the relevant Google search terms are "Wirtinger's algorithm" and "Wirtinger presentation." There's a really nice chapter of Rolfsen's "Knots and Links" that talks about coverings of $S^3 \setminus L$ using the fact that every oriented link in $S^3$ bounds a Seifert surface. | |
| Mar 15, 2023 at 19:54 | comment | added | Sam Nead | What is a (the?) "finite index universal abelian cover" of a manifold? | |
| S Mar 15, 2023 at 18:38 | review | First questions | |||
| Mar 15, 2023 at 18:45 | |||||
| S Mar 15, 2023 at 18:38 | history | asked | Mira T. | CC BY-SA 4.0 |