Timeline for 3-manifolds with all geodesics closed
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 10, 2018 at 19:40 | vote | accept | V. Rogov | ||
| Jan 9, 2018 at 21:13 | comment | added | Michael Albanese | The connected sum of $\mathbb{RP}^3$ with a non-trivial homology sphere is a non-trivial homology $\mathbb{RP}^3$. | |
| Jan 9, 2018 at 19:03 | history | edited | j.c. | CC BY-SA 3.0 |
add link to Bott's paper, minor spelling / grammar changes
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| Jan 9, 2018 at 18:54 | comment | added | Sam Nead | Ah - indeed, you have left out a hypothesis. Bott is assuming that all geodesics emanating from some special point $p$ are closed and simple. | |
| Jan 9, 2018 at 18:50 | answer | added | Sam Nead | timeline score: 7 | |
| Jan 9, 2018 at 18:48 | comment | added | Sam Nead | A nice quotient of the round three-sphere $S^3$ (say, a lens space) will have all geodesics closed, but need not have the homology of $S^3$ or of $P^3$. So I don't understand the statement that you attribute to Bott. | |
| Jan 9, 2018 at 18:20 | comment | added | Vesselin Dimitrov | Just to be sure: I assume you are aware of Arthur Besse's (old) extensive monograph on this subject? (Manifolds all of whose geodesics are closed, Ergeb. Math., vol. 91, 1976, 250 pp.) | |
| Jan 9, 2018 at 18:00 | history | asked | V. Rogov | CC BY-SA 3.0 |