Timeline for Relation between combinatorial manifolds and PL manifolds
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 21, 2012 at 1:43 | vote | accept | Malte | ||
| Jan 26, 2012 at 16:14 | answer | added | Junyan Xu | timeline score: 8 | |
| Jan 14, 2012 at 20:01 | comment | added | Malte |
This looks like a fine idea. I was wondering for a moment why this wouldn't work with an arbitrary atlas, but this is required as the intersection of two simplices $f_0: \Delta_0 \rightarrow M$ and $f_1: \Delta_1 \rightarrow M$ might otherwise be non-linear'' (I guess this is what you mean by make the transition maps linear''). Anyway, you're a very sweet man, thanks a lot!
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| Jan 13, 2012 at 18:54 | comment | added | Vitali Kapovitch | Perhaps I'm missing something but this seems clear to me. take a locally finite PL atlas and triangulate each chart linearly on some compact polyhedral domains that still cover M. Since the transition maps are PL and the cover is locally finite you can subdivide the triangulations to make the transition maps linear on simplexes. The resulting triangulation will obviously have spheres as links of vertices. | |
| Jan 13, 2012 at 17:57 | answer | added | Matt Brin | timeline score: 5 | |
| Jan 13, 2012 at 16:58 | history | asked | Malte | CC BY-SA 3.0 |