Timeline for Naive Reidemeister-Schreier for $\mathbb Z$ quotients
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 15, 2013 at 13:36 | comment | added | Lee Mosher | This is a comment on other methods outside of Reidemeister-Schreier. There is a dynamical systems method, based on "asymptotic cycles" or "homology directions" of flows, under which one shows that if you have one homomorphism to $\mathbb Z$ which fibers then so do all projectively nearby ones. This was used by Fried in his article in "Travaux de Thurston sur les surfaces", for understanding the dynamics of fibered facts of the Thurston norm on $H_2$ of a 3-manifold, but it applies more generally. | |
| Sep 15, 2013 at 7:33 | comment | added | HJRW | Right! I should have said 'Perhaps it's possible to upgrade this to the aspherical manifold setting using Davis-style Coxeter-group techniques.' | |
| Sep 14, 2013 at 16:31 | history | edited | Ryan Budney | CC BY-SA 3.0 |
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| Sep 14, 2013 at 16:28 | comment | added | Ryan Budney | I believe its uncomputable. And I want to use this algorithm on 4-manifold fundamental groups... So I can't avoid those problems. What I want to know is "can I get away with any more than I think I can?" | |
| Sep 14, 2013 at 6:38 | comment | added | HJRW | I'm not sure if you care, but it follows from Bestvina--Brady's work on combinatorial Morse theory that determining if a cyclic cover of a non-positively curved cube complex is finitely presentable is undecidable. Perhaps it's possible to upgrade this to the manifold setting using Davis-style Coxeter-group techniques. | |
| Sep 14, 2013 at 0:21 | history | asked | Ryan Budney | CC BY-SA 3.0 |