Complexes and Coxeter groups—Operations and outer automorphisms
نویسندگان
چکیده
منابع مشابه
Automorphisms of Coxeter Groups
We compute Aut(W ) for any even Coxeter group whose Coxeter diagram is connected, contains no edges labeled 2, and cannot be separated into more than 2 connected components by removing a single vertex. The description is given explicitly in terms of the given presentation for the Coxeter group and admits an easy characterization of those groups W for which Out(W ) is finite.
متن کاملOuter Automorphisms and the Jacobian
A graphs of rank n (homotopy equivalent to a wedge of n circles) without “separating edges” has a canonical n-dimensional compact C manifold thickening. This implies that the canonical homomorphism φ : Out(Fn) → GL(n,Z) is trivial in rational cohomology in the stable range answering a question raised in [6]. Another consequence of the construction is the existence of higher Reidemeister torsion...
متن کاملCoxeter Complexes and Graph-associahedra
Given a graph Γ, we construct a simple, convex polytope, dubbed graphassociahedra, whose face poset is based on the connected subgraphs of Γ. This provides a natural generalization of the Stasheff associahedron and the Bott-Taubes cyclohedron. Moreover, we show that for any simplicial Coxeter system, the minimal blow-ups of its associated Coxeter complex has a tiling by graph-associahedra. The ...
متن کاملAutomorphisms of nearly finite Coxeter groups
Suppose that W is an infinite Coxeter group of finite rank n, and suppose that W has a finite parabolic subgroup WJ of rank n 1. Suppose also that the Coxeter diagram of W has no edges with infinite labels. Then any automorphism of W that preserves reflections lies in the subgroup of AutðWÞ generated by the inner automorphisms and the automorphisms induced by symmetries of the Coxeter graph. If...
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1988
ISSN: 0021-8693
DOI: 10.1016/0021-8693(88)90163-9