VIRTUALLY FIBERING RIGHT-ANGLED COXETER GROUPS
نویسندگان
چکیده
منابع مشابه
A Complex for Right-angled Coxeter Groups
We associate to each right-angled Coxeter group a 2-dimensional complex. Using this complex, we show that if the presentation graph of the group is planar, then the group has a subgroup of finite index which is a 3-manifold group (that is, the group is virtually a 3-manifold group). We also give an example of a right-angled Coxeter group which is not virtually a 3-manifold group.
متن کاملInner Automorphisms of Right-angled Coxeter Groups
If W is a right-angled Coxeter group, then the group Aut(W ) of automorphisms of W acts on the set of conjugacy classes of involutions in W. Following Tits [16], the kernel of this action is denoted by Aut◦(W ). Since W is a CAT(0) group [12], the index of Aut◦(W ) in Aut(W ) is finite and there is a series 1 Inn(W ) Aut◦(W ) Aut(W ) of normal subgroups of Aut(W ). A presentation for Aut◦(W ) w...
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We show that right-angled Coxeter groups are relatively hyperbolic in the sense defined by Farb, relative to a natural collection of rank-2 parabolic subgroups.
متن کاملAutomorphisms of Right-Angled Coxeter Groups
If (W, S) is a right-angled Coxeter group, then Aut(W ) is a semidirect product of the group Aut◦(W ) of symmetric automorphisms by the automorphism group of a certain groupoid. We show that, under mild conditions, Aut◦(W ) is a semidirect product of Inn(W ) by the quotient Out◦(W ) = Aut◦(W )/Inn(W ). We also give sufficient conditions for the compatibility of the two semidirect products. When...
متن کاملRigidity of Right-angled Coxeter Groups
In mathematics, a group is the set of symmetries of an object. Coxeter groups are a broad and natural class of groups that are related to reflectional symmetries. Each Coxeter group is determined by a diagram, called a labeled graph, that encodes algebraic information about the group. In general, two different labeled graphs can give rise to the same group. It is therefore natural to ask: are t...
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ژورنال
عنوان ژورنال: Journal of the Institute of Mathematics of Jussieu
سال: 2019
ISSN: 1474-7480,1475-3030
DOI: 10.1017/s1474748019000422