Timeline for Topology of connected subsets of the $3$-torus
Current License: CC BY-SA 4.0
14 events
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| Jan 31, 2020 at 16:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Oct 3, 2019 at 15:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jun 5, 2019 at 15:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| May 6, 2019 at 16:49 | comment | added | Ryan Budney | "Half lives, half dies" is basically just an encoding of the restrictions put on maps due to Poincare duality. One way or another it's an encoding of the commutative ladder for the long exact sequence of a pair of manifolds. Generally it is most interesting around the middle dimension, which for 3-manifolds would be H^1 and H^2. | |
| May 6, 2019 at 11:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jan 6, 2019 at 11:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Dec 6, 2018 at 22:44 | answer | added | Klaas | timeline score: 1 | |
| Dec 6, 2018 at 17:44 | comment | added | Klaas | Thank you, this is interesting stuff! Can you expand a little on how this principle would help? In the Mayer Vietoris sequence there is only the difference of two such restriction maps. What makes me a bit skeptical is that my intuitive argument works in any dimension, that is, not just for the $3$-torus, whereas using the "half-lives, half-dies" principle would work only in dimension $3$ (or, any odd dimension?). | |
| Dec 6, 2018 at 8:08 | history | edited | Klaas | CC BY-SA 4.0 |
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| Dec 5, 2018 at 14:42 | comment | added | Danny Ruberman | You're on the right track with the Mayer-Vietoris sequence; have a look at the "half-lives, half-dies" principle. It tells you about the image of the restriction maps on $H^1$. Eg Lemma 3.5 of Hatcher's 3-manifold notes pi.math.cornell.edu/~hatcher/3M/3M.pdf. | |
| Dec 5, 2018 at 14:29 | history | edited | Klaas | CC BY-SA 4.0 |
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| Dec 5, 2018 at 14:19 | history | edited | Klaas | CC BY-SA 4.0 |
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| Dec 5, 2018 at 14:15 | review | First posts | |||
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| Dec 5, 2018 at 14:12 | history | asked | Klaas | CC BY-SA 4.0 |