Timeline for Normal generation of Torelli
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jun 6, 2012 at 4:32 | comment | added | Andy Putman | By the way, if you are interested in generating sets for Torelli, you might also be interested in my paper arxiv.org/abs/1106.3294. | |
| Jun 6, 2012 at 4:05 | comment | added | Igor Rivin | @Andy: yes, but since my original question was asking about a smaller presentation, Johnson certainly provides it (I was asking about this because the Torelli subgroup for free group autos has one normal generator, and it seemed reasonable that the same would hold here...) | |
| Jun 6, 2012 at 2:42 | comment | added | Andy Putman | @Igor Rivin (in response to your edit) : Johnson's paper uses the theorem of Powell. What he does is give relations in Torelli which express Powell's generators in terms of a single normal generator (a "genus 1 bounding pair map"). By the way, this requires $g \geq 3$, though it is clear from Powell's work that in genus $2$ that Torelli is generated by the normal closure of a single Dehn twist about a separating curve. In fact, in his thesis Mess proved that the genus $2$ Torelli group is a free group on an infinite set of Dehn twists about separating curves. | |
| Jun 6, 2012 at 0:38 | history | edited | Igor Rivin | CC BY-SA 3.0 |
found a better reference
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| Jun 4, 2012 at 22:11 | comment | added | Ian Agol | @Andy: Ok, I see. Here's a link to their paper: arxiv.org/abs/1110.0876 | |
| Jun 4, 2012 at 21:31 | vote | accept | Igor Rivin | ||
| Jun 4, 2012 at 21:17 | comment | added | Andy Putman | @Agol : It's pretty hard to extract generators from that paper except when $g=2$. The trouble is that the simplicial cpx they are using (the "cycle cpx") has a pretty complicated action of Torelli, and it is hard to work out eg the quotient. However, the paper "Generating the Torelli group" by Hatcher-Margalit uses the cycle cpx to prove that a different cpx (defined by me in my paper "A note on the connectivity of certain complexes associated to surfaces") is connected, and from this they get generators for Torelli. I originally proved this connectivity using generators for Torelli! | |
| Jun 4, 2012 at 19:18 | answer | added | Andy Putman | timeline score: 5 | |
| Jun 4, 2012 at 18:49 | comment | added | Ian Agol | You might be able to extract a presentation from this paper: ams.org/mathscinet-getitem?mr=2552249 | |
| Jun 4, 2012 at 18:16 | history | asked | Igor Rivin | CC BY-SA 3.0 |