Rigidity of skew-angled Coxeter groups
نویسندگان
چکیده
A Coxeter system is called skew-angled if its Coxeter matrix contains no entry equal to 2. In this paper we prove rigidity results for skew-angled Coxeter groups. As a consequence of our results we obtain that skew-angled Coxeter groups are rigid up to diagram twisting.
منابع مشابه
Rigidity 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...
متن کاملA Letter to the Seminario Teoria de Grupos
My friend and collaborator Mauricio Gutierrez asked me to record the following thoughts to provide a discussion point for your seminar. Herein I sketch an argument which proves the rigidity of right-angled Coxeter groups. The rigidity of right-angled Coxeter groups is a special case of the Even Rigidity Theorem which appears in Michael Laurence’s Ph.D. thesis [5] and Patrick Bahls’ Ph.D. thesis...
متن کاملAN ABSTRACT OF THE DISSERTATION OF Anton Kaul for the degree Doctor of Philosophy in Mathematics presented on May 3, 2000. Title: Rigidity for a Class of Coxeter Groups Abstract approved:
approved: William A. Bogley A Coxeter group W is said to be rigid if, given any two Coxeter systems (W,S) and (W,S ′), there is an automorphism ρ of W which carries S to S ′ In this dissertation we review rigidity results of D. Radcliffe [29] and of R. Charney and M. Davis [11], noting that certain restrictions must be placed on the Coxeter group in order to obtain rigidity. Radcliffe examined ...
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