Timeline for Homotopy type of an oriented, closed, simply connected manifold
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 5, 2016 at 12:21 | answer | added | Danny Ruberman | timeline score: 7 | |
| Jul 5, 2016 at 11:09 | comment | added | user83633 | Maybe the following paper is interesting to you: Schmitt, Alexander, On the classification of certain piecewise linear and differentiable manifolds in dimension eight and automorphisms of connected sums of (S2×S5). Enseign. Math. (2) 48 (2002), no. 3-4, 263–289. | |
| Jul 5, 2016 at 4:30 | comment | added | mme | You don't need to demand that things be so highly connected to have classification theorems; there is a (very difficult) classification theorem for simply connected 6-manifolds; see the manifold atlas. But this is already quite complicated, and if one for simply connected 8-manifolds is possible, it would be really very complicated indeed. Perhaps with some bravery one might dare to have a classification of 2-connected 8-manifolds. | |
| Jul 5, 2016 at 3:32 | comment | added | Qiaochu Yuan | I think you get an analogous result if you ask for it to be 3-connected. math.stanford.edu/~ksiegel/N-1Connected2NManifolds.pdf discusses a result of this form. | |
| Jul 5, 2016 at 2:58 | comment | added | David Roberts♦ | I think that a 4-manifold being simply connected, and the results that flow from that, could really a manifestation of the fact it is 4-3=1-connected. Hence for an 8-manifold you might find a nice result for 5-connected examples... | |
| Jul 5, 2016 at 0:17 | history | asked | Bilateral | CC BY-SA 3.0 |