Timeline for Examples of interesting non orientable closed 3-manifolds
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 28 at 19:18 | vote | accept | coudy | ||
| Sep 21, 2017 at 4:48 | comment | added | Ryan Budney | @ThiKu: the Gieseking manifold isn't closed, and its volume is half the figure-8 exterior. The figure-8 exterior is the double-cover of the Gieseking.. . although, the Gieseking is also quite an interesting 3-manifold. | |
| Sep 20, 2017 at 15:33 | comment | added | Ian Agol | @coudy: I just meant the snappea census, which was originally carried out by Weeks, and is incorporated into SnapPy. I linked to a paper which mentions this manifold. | |
| Sep 20, 2017 at 15:32 | history | edited | Ian Agol | CC BY-SA 3.0 |
added 114 characters in body
|
| Sep 20, 2017 at 15:22 | comment | added | Ian Agol | @ThiKu: It's possible that one can deduce this from their paper, but for some reason they don't formulate a theorem of this sort. I suppose one would just need an equivariant connect-sum decomposition of the 2-fold orientable cover, which ought to follow from Meeks-Yau. One also needs to know that involutions of Haken manifolds preserve the geometric decomposition, which should be okay. Then deduce that it is an isometry on each geometric piece from their theorems, and glue up along the JSJ and connect sum decompositions. | |
| Sep 20, 2017 at 14:56 | comment | added | coudy | There is a Python package that contains information about the aforementioned manifold. math.uic.edu/t3m/SnapPy/censuses.html Any link to the Weeks census? | |
| Sep 20, 2017 at 14:55 | comment | added | Ian Agol | No, it's not the Gieseking. | |
| Sep 20, 2017 at 14:55 | comment | added | ThiKu | About Ricci Flow: it seems to me that the work of Dinkelbach-Leeb on equivariant Ricci flow doesn't make orientability assumptions: arxiv.org/pdf/0801.0803.pdf So it should prove geometrization in the nonorientable case or am I missing something? | |
| Sep 20, 2017 at 14:50 | comment | added | ThiKu | en.wikipedia.org/wiki/Gieseking_manifold | |
| Sep 20, 2017 at 14:50 | comment | added | ThiKu | For the last paragraph: you are probably referring to the Gieseking manifold, whose volume is half of that of the figure eight knot complement and which in fact is 2-fold covered by the figure eight knot complement. | |
| Sep 20, 2017 at 14:43 | history | answered | Ian Agol | CC BY-SA 3.0 |