An effective compactness theorem for Coxeter groups
نویسندگان
چکیده
منابع مشابه
An Effective Compactness Theorem for Coxeter Groups
Through highly non-constructive methods, works by Bestvina, Culler, Feighn, Morgan, Rips, Shalen, and Thurston show that if a finitely presented group does not split over a virtually solvable subgroup, then the space of its discrete and faithful actions on Hn, modulo conjugation, is compact for all dimensions. Although this implies that the space of hyperbolic structures of such groups has fini...
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Coxeter groups have presentations 〈S : (st)st∀s, t ∈ S〉 where for all s, t ∈ S, mst ∈ {1, 2, . . . ,∞}, mst = mts and mst = 1 if and only if s = t. A fundamental question in the theory of Coxeter groups is: Given two such “Coxeter” presentations, do they present the same group? There are two known ways to change a Coxeter presentation, generally referred to as twisting and simplex exchange. We ...
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A finite Coxeter group possesses a distinguished conjugacy class of Coxeter elements. The literature about these is very large, but it seems to me that there is still room for a better motivated account than what exists. The standard references on thismaterial are [Bourbaki:1968] and [Humphreys:1990], butmy treatment follows [Steinberg:1959] and [Steinberg:1985], from which the clever parts of ...
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A finite complete rewriting system for a group is a finite presentation which gives a solution to the word problem and a regular language of normal forms for the group. In this paper it is shown that the fundamental group of an orientable closed surface of genus g has a finite complete rewriting system, using the usual generators a1, .., ag, b1, .., bg along with generators representing their i...
متن کاملArtin Groups and Coxeter Groups
where the words on each side of these relations are sequences of mij letters where ai and aj alternate in the sequence. The matrix of values mij is a Coxeter matrix M = (mij)i,j∈I on I. These groups generalize the braid groups established in 1925 by E. Artin in a natural way and therefore we suggest naming them Artin groups. If one adds the relations ai = 1 to the relations in the presentation ...
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2009
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-009-9416-8