Timeline for Does there exist infinitely many prime knots?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Sep 8, 2020 at 22:32 | answer | added | Pablo S. Ocal | timeline score: 2 | |
| Nov 23, 2011 at 3:28 | comment | added | Daniel Moskovich | These notes give a basic exposition of the infinity of prime knots, and Schubert's proof of uniqueness of prime factorization: math.ucla.edu/~radko/191.1.05w/marcos.pdf | |
| Nov 23, 2011 at 2:01 | comment | added | Ryan Budney | It's a theorem of Schubert's from the 1930's that oriented knots under the connect-sum operation are a free commutative monoid on infinitely many generators. | |
| Nov 22, 2011 at 20:07 | comment | added | Steven Sivek | Knots do decompose uniquely into a sum of primes, see e.g. chapter 2 of Lickorish's "An introduction to knot theory." Also, since knot genus is additive under connected sum it follows that every genus 1 knot is prime, so take your favorite knot and consider all of its twisted Whitehead doubles; these have genus 1 and are distinguished by their Alexander polynomials. | |
| Nov 22, 2011 at 19:29 | answer | added | Jana Archibald | timeline score: 14 | |
| Nov 22, 2011 at 19:16 | comment | added | Qiaochu Yuan | Yes; in fact there are infinitely many distinct torus knots, all of which are prime (en.wikipedia.org/wiki/Torus_knot). | |
| Nov 22, 2011 at 19:13 | history | asked | 36min | CC BY-SA 3.0 |