#19594: Implement the cactus group
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Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.0
Component: group theory | Resolution:
Keywords: cactus | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/groups/cactus_group-19594 | 7eb2a1278ea0ca08375f87e0f82081218a2ea1ec
Dependencies: | Stopgaps:
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Comment (by dimpase):
Replying to [comment:21 tscrim]:
> `s14 |-> (1,4) (2,3)` is the correct image as `s14` should correspond to
flipping the entire interval `[1, 4]`.
oops, OK then. Sorry for noise. By the way, what is proper Sage way to get
words generating
the kernel of the homomorphism to S_n?
>
> I asked Peter Tingley, who asked Joel Kamnitzer, and they do not know of
a normal form.
>
> What do both of you think about trying to prove an analog of Matsumoto's
theorem for the cactus group, i.e., that all reduced words are related to
each other by just applying the defining relations, as per comment:15?
this looks a bit unlikely that a Matsumoto's-type argument would work
here, with so many redundant generators (as opposed to the case of Coxeter
groups). What might work is a kind of argument one sees for presentations
of soluble groups, where one has commutator relations, allowing one to
"sort" generators in words; but as we have S_n acting, unsolvable for
n>4...
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Ticket URL: <http://trac.sagemath.org/ticket/19594#comment:23>
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