I'd like to know if there exists (and, in this case, where I can find it) some computer program/programming language/any kind of software that can find explicitly the conetypes of a hyperbolic group on which I am working (a presentation of which is known).


1 Answer 1


My KBMAG package can compute a finite state automaton that accepts the language of geodesic words in a hyperbolic group, and I think the states of that automaton correspond exactly to the conetypes.

It is not particularly easy to use. If you write down the presentation of the group you are interested in, then I can try out the computation for you.

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    $\begingroup$ Thank you very much for your kindness, but the computations I need to perform actually involve couples of conetypes in quite a strange way... I'll try another way out. The group is the well known $\Gamma_2=\langle a_1,b_1,a_2,b_2\mid [a_1,b_1][a_2,b_2]\rangle$, the number of conetypes is known and should amount to $49$ (according to some papers); I think it should be possible to them down by hand... Actually, I needed just a confirmation. PS: I'm really sorry for the delay in my answer! $\endgroup$
    – EM90
    Commented Sep 28, 2015 at 15:51
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    $\begingroup$ Yes, my computer calculation, which only took a second or two, also gave the answer $49$ contypes. $\endgroup$
    – Derek Holt
    Commented Sep 28, 2015 at 17:06

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