#20154: train-tracks
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Reporter: dbenielli | Owner:
Type: task | Status: new
Priority: major | Milestone: sage-7.1
Component: combinatorics | Resolution:
Keywords: free-group automorphism | Merged in:
Authors: Dominique Benielli and | Reviewers:
Thierry Coulbois | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Changes (by tscrim):
* cc: tscrim (added)
* keywords: free-group automorphisme => free-group automorphism
Old description:
> We propose to implement in Sage the train-tracks package developped by
> Thierry Coulbois:
>
> The main feature and the main achievement of the program is to compute
> train- track representative for (outer) automorphisms of free groups.
> phi.train track() computes a train-track representative for the (outer)
> automorphism phi. This train-track can be either an absolute train-track
> or a relative train-track. The celebrated theorem of Bestvina and Feighn
> [?] assures that if phi is fully irre- ducible (iwip) then there exists
> an absolute train-track representing phi.
> The train-track(relative=False) method will terminate with either an
> absolute train-track or with a topological representative with a
> reduction: an invariant strict subgraph with non-trivial fundamental
> group.
> One more feature of train-tracks (absolute or relative) is to lower the
> number of Nielsn paths. Setting the stable=True option will return a
> train-track with at most one indivisible Nielsen path (per exponential
> stratum if it is a relative train-track).
New description:
We propose to implement in Sage the train-tracks package developed by
Thierry Coulbois:
The main feature and the main achievement of the program is to compute
train-track representative for (outer) automorphisms of free groups.
phi.train track() computes a train-track representative for the (outer)
automorphism phi. This train-track can be either an absolute train-track
or a relative train-track. The celebrated theorem of Bestvina and Feighn
assures that if phi is fully irreducible (iwip), then there exists an
absolute train-track representing phi.
The train-track(relative=False) method will terminate with either an
absolute train-track or with a topological representative with a
reduction: an invariant strict subgraph with non-trivial fundamental
group.
One more feature of train-tracks (absolute or relative) is to lower the
number of Nielsen paths. Setting the stable=True option will return a
train-track with at most one indivisible Nielsen path (per exponential
stratum if it is a relative train-track).
See also:
- https://github.com/coulbois/sage-train-track
- https://www.i2m.univ-amu.fr/~coulbois/train-track/
--
Comment:
Let me know if you have any questions or if there is anything I can do to
help.
In case you were unaware, you might also be interested in that Sage has an
implementation of right-angled Artin groups.
--
Ticket URL: <http://trac.sagemath.org/ticket/20154#comment:2>
Sage <http://www.sagemath.org>
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