Timeline for Examples of manifolds that do not admit scalar flat metrics
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Feb 1, 2019 at 4:38 | vote | accept | Ryan Unger | ||
| Feb 1, 2019 at 4:38 | answer | added | Ryan Unger | timeline score: 4 | |
| Mar 18, 2018 at 3:44 | comment | added | Michael Albanese | For $n \equiv 2 \bmod 8$, there are examples similar to the ones mentioned by Igor Belegradek (see my comment on his answer). So the only dimensions that have not been covered so far are $n \equiv 3, 5, 6, 7 \bmod 8$. | |
| Mar 13, 2018 at 3:47 | comment | added | Michael Albanese | Note that $(T^4\# K3)^m$ is a $4m$-dimensional manifold in class (C) using the same criterion. So the missing dimensions are $n \equiv 2, 3, 5, 6, 7 \bmod 8$. By the classification of manifolds in class (A) mentioned in Igor Belegradek's answer, if $n \equiv 3, 5, 6, 7 \bmod 8$, any $n$-manifold in class (C) has non-trivial fundamental group. | |
| Mar 3, 2018 at 21:49 | history | edited | Ryan Unger | CC BY-SA 3.0 |
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| Mar 3, 2018 at 21:44 | history | edited | Ryan Unger | CC BY-SA 3.0 |
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| Mar 3, 2018 at 21:18 | answer | added | Igor Belegradek | timeline score: 7 | |
| Mar 3, 2018 at 20:59 | answer | added | Michael Albanese | timeline score: 11 | |
| Mar 3, 2018 at 19:45 | history | asked | Ryan Unger | CC BY-SA 3.0 |