Timeline for Extending smooth triangulation
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 22 at 9:32 | comment | added | shuhalo | You mention a result by Munkres on smooth separating hypersurfaces, which I presume is in his textbook. Do you know whether it extends to topological separating hypersurfaces? | |
| Aug 3, 2020 at 12:01 | comment | added | Igor Belegradek | A good example is PL knotted ball pair $(B^4, B^2)$ that is the cone on a nontrivial knot in $S^3$. There is of course a triangulation of $B^4$ that restricts to a triangulation of $B^2$ but if we triangulate $B^2$ as a simplex, this triangulation does not extend to a triangulation of $B^4$ because it does not capture the local knottedness at the cone point. | |
| Aug 3, 2020 at 11:20 | comment | added | Igor Belegradek | @MarkGrant: it is not the same. An exercise in Munkres' "Elementary Differential topology", and probably, a theorem in Verona's book in your linked answer says that there is a smooth triangulation of $M$ in which $S$ is a subcomplex. What I ask for is to extend a smooth triangulation of $S$ to a smooth triangulation of $M$. I don't want to change the given triangulation of $S$. I do not want to subdivide it. | |
| Aug 3, 2020 at 7:53 | comment | added | Mark Grant | Is this the same as this question mathoverflow.net/q/206212/8103? | |
| Aug 3, 2020 at 2:12 | history | edited | Igor Belegradek | CC BY-SA 4.0 |
added 13 characters in body
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| Aug 2, 2020 at 23:59 | history | asked | Igor Belegradek | CC BY-SA 4.0 |