Timeline for Extension of covering map
Current License: CC BY-SA 4.0
4 events
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| Mar 26, 2022 at 12:00 | history | edited | Ian Agol | CC BY-SA 4.0 |
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| Oct 8, 2012 at 4:06 | comment | added | Ian Agol | @Igor: agreed. There may be some shortcuts given the extra information you have about the covering space induced of the boundary. For example, if you're considering $M, N$ handlebodies, then the cover $\partial M\to \partial N$ will determine a unique cover $M\cong \tilde{N}\to N$ which induces the cover of the boundary (if it exists - one just has to check that curves in $N$ bounding disks lift). In this case, I think a reasonable algorithm might exist, basically reducing to Haken's algorithm, or Whitehead's algorithm, depending on how the handlebodies are given. | |
| Oct 8, 2012 at 1:06 | comment | added | Igor Rivin | That's certainly enlightening, and it is good to know that the solution is algorithmic, but not very satisfying, on a number of levels (e.g. the first step of checking all possible homomorphisms to $S_n$ does not thrill...) | |
| Oct 8, 2012 at 0:23 | history | answered | Ian Agol | CC BY-SA 3.0 |