Timeline for Applications of knot theory
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| S Dec 25, 2015 at 18:20 | history | suggested | CommunityBot | CC BY-SA 3.0 |
Fixed MathJax
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| Dec 25, 2015 at 18:06 | review | Suggested edits | |||
| S Dec 25, 2015 at 18:20 | |||||
| Apr 5, 2012 at 8:29 | history | edited | Ryan Budney | CC BY-SA 3.0 |
mixed-up terminology of symmetric product and space of finite subsets
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| Dec 5, 2010 at 17:04 | comment | added | Sam Nead | I would classify this more as "further reading/advanced topics" than as an "application". But it is very nice. Are there similar configuration space constructions giving Seifert fiberings of $S^3$ or of other manifolds? | |
| Dec 4, 2010 at 18:34 | comment | added | Ryan Budney | Symmetric products are a common construction in algebraic topology, try a google search on "infinite symmetric product". The Moebius band example is a well-known one as there's a canonical embedding of $(S^1)^2/\Sigma_2$ in the space of straight lines in $\mathbb R^2$ which is a Moebius band (given a line in the plane intersect it with the unit circle) -- the space of straight lines in $\mathbb R^2$ is the canonical/classifying bundle over $\mathbb RP^1$, for example. This is in Milnor and Stasheff's book on characteristic classes. | |
| Dec 4, 2010 at 18:12 | comment | added | Michael Hardy | If anyone cares, I've started a discussion on how to organize Wikipedia's material on symmetric products: en.wikipedia.org/wiki/… | |
| Dec 4, 2010 at 17:41 | comment | added | Michael Hardy | I don't know if I've run across the term "symmetric product" before, but it seems just about self-explanatory. I recall seeing a paper in the American Mathematical Monthly that said (in the language used in the answer above, but not in the paper I saw, as far as I recall) that the symmetric product of the circle with itself is the Möbius band. Is that well-known to topologists? Wikipedia's article en.wikipedia.org/wiki/Symmetric_product_of_an_algebraic_curve limits the concept to algebraic curves. Should it get edited to make it more general, or should there be a separate article? | |
| Dec 3, 2010 at 23:22 | history | edited | Ryan Budney | CC BY-SA 2.5 |
Jose
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| Dec 3, 2010 at 23:20 | comment | added | José Figueroa-O'Farrill | I think you missed a superscript $^3$ in your first displayed equation. | |
| Dec 3, 2010 at 23:00 | history | answered | Ryan Budney | CC BY-SA 2.5 |