Timeline for Reducible 3d torus bundles
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 16, 2009 at 16:19 | vote | accept | janmarqz | ||
| Dec 16, 2009 at 16:19 | history | bounty ended | janmarqz | ||
| Dec 14, 2009 at 0:58 | comment | added | janmarqz | @Sam: 10-4, gonna check, super-thanks | |
| Dec 14, 2009 at 0:39 | history | edited | Sam Nead | CC BY-SA 2.5 |
Mention SL(2,Z).
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| Dec 11, 2009 at 1:23 | comment | added | janmarqz | for a torus bundle $T\subset E\to S^1$ we have that $\pi_1(T)$ is a normal subgroup of $\pi_1(E)=\pi_1(T)*_{Z}Z$ and if $\pi_1(E)$ could split freely then $\pi_1(T)$ would split freely too, which is ridiculous. So $\pi_1(E)$ can't freely splitted and then $E$ can't be a connected sum... | |
| Dec 8, 2009 at 21:50 | comment | added | Sam Nead | @Juan - I would guess that there is also a proof along these lines. I would also guess that there are some details to fill-in here. For example, there certainly are HNN extensions that decompose as free products... | |
| Dec 8, 2009 at 21:42 | history | edited | Sam Nead | CC BY-SA 2.5 |
added 40 characters in body
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| Dec 8, 2009 at 21:37 | comment | added | janmarqz | non trivial F-surface bundles M have $\pi_1(M)=\pi_(F)*_{Z}Z$ which isn't a free product so it can't be reducible (in the sense of connected sum) and were the amalgamation is the group generated by the isotopy class of the auto-homeomorph... | |
| Dec 8, 2009 at 20:08 | history | answered | Sam Nead | CC BY-SA 2.5 |