Timeline for Monotone invariants of braid forcing
Current License: CC BY-SA 3.0
8 events
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| Oct 1, 2011 at 6:33 | comment | added | Danny Calegari | @Agol: essentially all the invariants discussed in Ghys' paper (eg helicity, Ruelle invariant, Calabi quasimorphism etc.) as well as many variations (Polterovich, Py, etc.) are obtained by taking some local topological invariant of the dynamics on finitely many points, and integrating it over the degrees of freedom of the choice of the finitely many points wrt an invariant measure. If you take any braid type and "shrink" the dynamics down to be concentrated in a very small disk, the value of these invariants typically goes to zero. Did you have any specific part of the paper in mind? | |
| Oct 1, 2011 at 2:05 | comment | added | Ian Agol | You might have a look at Ghys' 2006 ICM talk: icm2006.org/proceedings/Vol_I/15.pdf | |
| Sep 30, 2011 at 21:47 | history | edited | Danny Calegari | CC BY-SA 3.0 |
removed bizarre .png that someone inserted in place of some TeX
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| Feb 16, 2010 at 14:58 | history | edited | Steve Huntsman |
arxiv tag
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| Nov 12, 2009 at 14:56 | comment | added | Danny Calegari | (So for instance, the "empty braid" is forced by everything) | |
| Nov 12, 2009 at 6:00 | comment | added | Danny Calegari | Yes, if the strands you erase (or, equivalently, keep) are a union of orbits of the diffeomorphism. In other words, if $Q$ is a finite subset permuted by $\phi$, and $P$ is a subset of $Q$ invariant under $\phi$ then erasing (or keeping) $Q$ gives you a new braid (which is forced by the original braid). | |
| Nov 12, 2009 at 5:50 | comment | added | JSE | Naive question: I draw a picture of a braid on n strands and then erase n-m of the strands. Is the resulting m-strand braid "forced: by the original braid in your sense? | |
| Nov 12, 2009 at 1:46 | history | asked | Danny Calegari | CC BY-SA 2.5 |