Timeline for Extension of homeomorphisms on a spherical space
Current License: CC BY-SA 2.5
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| Dec 15, 2010 at 0:52 | history | edited | Tomas Paul | CC BY-SA 2.5 |
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| Dec 15, 2010 at 0:52 | comment | added | Andy Putman | No. For example, let $X \subset S^3$ be a closed tubular neighborhood of the unknot. Thus $X$ is a solid torus (ie $D^2 \times S^1$) and $S^3 \setminus X$ is the interior of a solid torus. Let $f : X \rightarrow X$ be the homeomorphism obtained by cutting $X$ open along the disc $D^2 \times 1$, giving the cut open space a full twist, and regluing. Then it is easy to see that $f$ does not extend to a homeomorphism of $S^3$. | |
| Dec 15, 2010 at 0:36 | history | asked | Tomas Paul | CC BY-SA 2.5 |