Timeline for Cohomology ring of mapping torus
Current License: CC BY-SA 4.0
13 events
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| Apr 10, 2022 at 2:56 | comment | added | Ian Gershon Teixeira | When $ \phi $ is finite order, associated to Euclidean geometry, the mapping tori are Seifert Fibred. But it is worth noting that the the mapping tori of $ T^2 $ are also Seifert Fibred when the mapping class has the form $ \begin{bmatrix} 1 & k\\ 0 & 1 \end{bmatrix} $, associated to Nil geometry, as given in the answer by Vitali Kapovitch ( in this case the Seifert fibration is actually a regular fibre bundle, indeed it is even a $ U_1 $ principal circle bundle). Several very detailed and beautiful answers are given herehttps://math.stackexchange.com/a/3791368/758507 | |
| Apr 10, 2022 at 1:42 | history | edited | Xiao-Gang Wen |
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| Apr 10, 2022 at 1:29 | history | edited | Xiao-Gang Wen | CC BY-SA 4.0 |
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| Apr 8, 2022 at 19:57 | answer | added | jdc | timeline score: 7 | |
| Apr 8, 2022 at 18:48 | history | became hot network question | |||
| Apr 8, 2022 at 18:46 | answer | added | Vitali Kapovitch | timeline score: 10 | |
| Apr 8, 2022 at 17:44 | comment | added | Ryan Budney | The answers so far are describing the group structure. The ring structure is one level of detail beyond this. Although it does not answer your question, you might want to check out some Peter Svengrowski papers, where he works out the cohomology ring structure for Seifert Fibred 3-manifolds. In the case $\phi$ is finite order, your mapping tori are Seifert Fibred, so they will appear in his work. | |
| Apr 8, 2022 at 15:50 | answer | added | R. van Dobben de Bruyn | timeline score: 11 | |
| Apr 8, 2022 at 15:05 | history | edited | Sam Nead | CC BY-SA 4.0 |
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| Apr 8, 2022 at 14:26 | history | edited | Sam Nead | CC BY-SA 4.0 |
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| Apr 8, 2022 at 14:10 | answer | added | Nick L | timeline score: 9 | |
| Apr 8, 2022 at 8:10 | comment | added | Ryan Budney | Mostly it's pretty degenerate. Probably the most useful way to structure the computation would be the Thurston geometry approach, i.e. break it into the Anosov case vs. fixing a curve vs. finite order. | |
| Apr 7, 2022 at 23:51 | history | asked | Xiao-Gang Wen | CC BY-SA 4.0 |