Timeline for When does a subgroup H of a group G have a complement in G?
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| Nov 14, 2009 at 22:16 | comment | added | Tom Church | 1) "you can do an extension calculation to see if it exists." Well, unless you already know the group cohomology of the quotient for some other reason, checking whether the extension cocycle is trivial in H^2 is exactly as difficult as finding a complement by hand, so I don't know that "calculation" is the best word. Certainly this approach is often very useful anyway. 2) just to clarify, the complement to SO(n) in SO+(n,1) doesn't stabilize any single horosphere; it stabilizes a family of concentric horospheres. | |
| Nov 14, 2009 at 17:15 | history | answered | Greg Kuperberg | CC BY-SA 2.5 |