Timeline for Topological Classification of Four-Manifolds
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 25, 2018 at 0:46 | comment | added | QGravity | Thank you very much, your answer and comment are very helpful. Based on your comment, I think one then need to understand what sort of topological constraints come from the global hyperbolicity condition on four-manifolds regarded as space-time in physics. I only heard that the only constraint is that the space-time can be written as $\mathbb{R}\times X$, where $X$ is a compact three-manifold and consider the topological classification of compact three-manifolds (possibly with boundary), but I am not sure. | |
| Feb 22, 2018 at 9:57 | comment | added | Daniele Zuddas | It is a classical result that finitely presented groups cannot be algorithmically classified. Then, it is not possible to classify smooth 4-manifolds if you do not put some (actually strong) topological or geometric restrictions. The same holds for 4-manifolds with boundary. | |
| Feb 21, 2018 at 21:07 | comment | added | QGravity | In physics, the people are more interested to consider compact four-manifolds with boundaries (which might have some sort of "topological singularity" representing singular behavior in space-time like black hole singularity or big bang). I was very curious about the development in the topological classification of such four-manifolds. | |
| Feb 21, 2018 at 21:01 | comment | added | QGravity | So, isn't it possible to classify finitely-presented groups just like finitely-generated Fuchsian groups? | |
| Feb 21, 2018 at 20:54 | vote | accept | QGravity | ||
| Feb 21, 2018 at 20:55 | |||||
| Feb 21, 2018 at 15:01 | history | answered | Daniele Zuddas | CC BY-SA 3.0 |