Timeline for Open non-parallelizable 4-manifolds
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 17, 2016 at 2:04 | comment | added | Danny Ruberman | @Ryan: Perhaps a more natural construction is to take a compact non-orientable surface (with a Riemannian metric) $\times R^2$ where the latter has the Minkowski metric. This version is (presumably--I don't know much about Lorentz metrics) complete. | |
| May 16, 2016 at 22:42 | vote | accept | Michael | ||
| May 16, 2016 at 22:02 | comment | added | Igor Belegradek | It seems the wikipedia article assumes the manifold is spin, in which case there is no $w_2$. It says: "Usually, one also requires that a world manifold admits a spinor structure in order to describe Dirac fermion fields in gravitation theory. There is the additional topological obstruction to the existence of this structure. In particular, a noncompact world manifold must be parallelizable." | |
| May 16, 2016 at 22:00 | comment | added | Ryan Budney | I suppose taking a non-orientable 3-manifold and building the orientable (total space) $S^1$-bundle over it would give you a non-parallelizable lorentzian manifold. You could then puncture it once to make it open. | |
| May 16, 2016 at 21:58 | history | answered | Danny Ruberman | CC BY-SA 3.0 |