Timeline for Linking topological spheres
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 20, 2019 at 15:49 | comment | added | Ian Agol | see en.wikipedia.org/wiki/Homology_sphere?wprov=sfti1 The Brieskorn spheres might be the easiest to describe. When $(p,q,r)$ satisfy $1/p+1/q+1/r \leq 1$, $\Sigma(p,q,r)$ will have infinite fundamental group. | |
| Jan 20, 2019 at 15:26 | comment | added | Piotr Hajlasz | @IanAgol Thank you for your nice comment. Where can I find an example of a homology 3-sphere with infinite $\pi_1$? (I am not a topologist, but an analyst who is using topology in their research; topology is a shaky ground for me). | |
| Jan 20, 2019 at 2:40 | comment | added | Ian Agol | Even though I’m well aware of Cannon-Edwards’ result, this answer still surprised me. Smoothly embedded circles in 4 dimensions and higher are unknotted, so this example is quite counterintuitive, in some sense it can’t be well-approximated by smooth circles. Using other homology 3-spheres with infinite $π_1$, you get examples where any embedded 3-sphere must have linking number 0, since a 3-sphere can have a finite degree map only to a manifold with finite fundamental group. | |
| Jan 19, 2019 at 18:30 | history | edited | Piotr Hajlasz | CC BY-SA 4.0 |
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| Nov 25, 2018 at 20:16 | history | edited | Piotr Hajlasz | CC BY-SA 4.0 |
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| Nov 25, 2018 at 19:52 | history | answered | Piotr Hajlasz | CC BY-SA 4.0 |