Timeline for Sections of topological group extensions
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 3, 2011 at 3:36 | vote | accept | gurs | ||
| Jan 1, 2011 at 9:44 | history | edited | David Roberts♦ | CC BY-SA 2.5 |
Clarified question by inserting OP's own comments.
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| Jan 1, 2011 at 8:43 | vote | accept | gurs | ||
| Jan 1, 2011 at 8:43 | |||||
| Dec 31, 2010 at 18:16 | comment | added | Anton Geraschenko | gurs says (moved from an answer): Can someone give an example in the setting of compact topological groups or in the setting of finite dimensional Banach spaces. | |
| Dec 24, 2010 at 12:11 | comment | added | Theo Buehler | @Johannes: While this is nice, gurs wants a non-split extension. | |
| Dec 24, 2010 at 10:06 | comment | added | Johannes Ebert | Take the extension $1 \to \mathbb{R} \to \mathbb{R}^2 \to \mathbb{R} \to 0$ and the section $x \mapsto (x,x^3)$. | |
| Dec 24, 2010 at 9:54 | answer | added | Theo Buehler | timeline score: 10 | |
| Dec 24, 2010 at 9:13 | comment | added | gurs | Let me write my question again. Does there exist an extension of topological groups $1 \to N \to E \to G \to 1$ admitting a section $s:G \to E$ which is continuous (or only continous in a neighbourhood of identity) and satisfy the property that $s(x^{-1})=s(x)^{-1}$ for all $x \in G$ but is not a homomorphism. | |
| Dec 24, 2010 at 9:04 | comment | added | gurs | Thanks. But I want a non-trivial extension. | |
| Dec 24, 2010 at 8:36 | comment | added | David Roberts♦ | Yes: a semi-direct product. Or do you want some sort of non-triviality condition? | |
| Dec 24, 2010 at 8:14 | history | asked | gurs | CC BY-SA 2.5 |