Timeline for Your favorite surprising connections in mathematics
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
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| Sep 1, 2019 at 7:06 | comment | added | Ryan Budney | @DanRamras, apologies, I somehow conflated the two spaces. Delete my 2nd sentence -- those two aren't quite the same. | |
| Sep 1, 2019 at 1:51 | comment | added | Dan Ramras | @RyanBudney I'm confused by the claim that $SS_3 (S^1)$ is the 3-sphere. If $SS_3 (S^1)$ is really the same as the symmetric product $(S^1)^3/\Sigma_3$, then there are maps $S^1\to (S^1)^3/\Sigma_3 \to S^1$ defined by $z \mapsto [z, 1, 1]$ and $[x, y, z]\mapsto xyz$ which compose to the identity. So $(S^1)^3/\Sigma_3$ isn't simply connected. | |
| Mar 10, 2017 at 9:42 | history | edited | CommunityBot |
replaced http://upload.wikimedia.org/ with https://upload.wikimedia.org/
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| Mar 13, 2011 at 22:12 | comment | added | Sam Nead | Ah - here is the question I saw - mathoverflow.net/questions/22138/… | |
| Mar 13, 2011 at 22:08 | comment | added | Sam Nead | Your claim about taking the link of the singular point of the hypersurface $x^2 + y^2 + z^2 + w^3 = 0$, and getting an exotic five-sphere, sounds wrong to me. Is there a reference for this? | |
| Mar 13, 2011 at 19:40 | history | edited | Sputnik | CC BY-SA 2.5 |
Typo.
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| Mar 13, 2011 at 19:01 | history | edited | darij grinberg | CC BY-SA 2.5 |
fixed typo
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| Aug 16, 2010 at 0:00 | comment | added | Ryan Budney | There's an interesting related result -- let $SS_n(X)$ denote the space of subsets of a topological space $X$ where the subsets have cardinality between $1$ and $n$. As a space, you can consider it to be $X^n / \Sigma_n$. Then $SS_3(S^1)$ is the 3-sphere. By design, $SS_n(S^1)$ has a fixed-point free $SO_2$-action, so it's a Seifert-fibred space. A non-singular orbit of this $SO_2$-action on $SS_3(S^1)$ is the trefoil knot. | |
| Jul 15, 2010 at 19:55 | comment | added | The Mathemagician | Wow,that IS pretty whack,Csar.This example alone is a testament to the power of modern topology and geometry and the incredible connections it has uncovered. | |
| Feb 17, 2010 at 1:16 | history | edited | Csar Lozano Huerta | CC BY-SA 2.5 |
added 25 characters in body
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| Feb 16, 2010 at 22:35 | history | answered | Csar Lozano Huerta | CC BY-SA 2.5 |