Timeline for Prime decomposition for knots in manifolds
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Apr 7, 2010 at 19:38 | comment | added | Ryan Budney | There is a 2-cubes/discs action for "knots" in a variety of 3-manifolds but they're maybe not what most people would like to call knots. Things like self-embeddings of $\mathbb{R}\times \Sigma$ in itself with support contained in $[-1,1]\times \Sigma$ where $\Sigma$ is a compact 2-manifold. Presumably there's more global algebraic structure lurking in the background for general knots in 3-manifolds but I haven't found a strong formalism for it. | |
| Apr 7, 2010 at 13:01 | answer | added | Steven Sivek | timeline score: 9 | |
| Apr 7, 2010 at 7:02 | comment | added | Daniel Moskovich | @Ryan- I would ask also whether there is a little discs operad action in such a context. What would happen with your work with Fred Cohen for long knots in other 3-manifolds? | |
| Apr 7, 2010 at 6:46 | comment | added | John Vrem | Perhaps that will work. But even better to say: this raises another question, namely what all possible definitions of connected sum(s) are! | |
| Apr 7, 2010 at 6:20 | comment | added | Ryan Budney | What definition of connect-sum do you want to use? I suppose the most natural one would be to take connect-sum of the ambient manifolds along common 3-balls that intersect the knots in unknotted arcs. Is that what you're interested in? | |
| Apr 7, 2010 at 5:50 | history | asked | John Vrem | CC BY-SA 2.5 |