Piecewise Linear Groups and Transformation Groups
نویسندگان
چکیده
منابع مشابه
Groups of Piecewise Linear Homeomorphisms
In this paper we study a class of groups which may be described as groups of piecewise linear bijections of a circle or of compact intervals of the real line. We use the action of these groups on simplicial complexes to obtain homological and combinatorial information about them. We also identify large simple subgroups in all of them, providing examples of finitely presented infinite simple gro...
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In this paper, in addition to some elementary facts about the ultra-groups, which their structure based on the properties of the transversal of a subgroup of a group, we focus on the relation between a group and an ultra-group. It is verified that every group is an ultra-group, but the converse is not true generally. We present the conditions under which, for every normal subultra-group of an u...
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We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows ua to easily recover centralizers and lends itself to generalization.
متن کاملThe Simultaneous Conjugacy Problem in Groups of Piecewise Linear Functions
Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson’s group F . We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to so...
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We construct some non-essential H-closed epireflections of W, the category of archimedean l-groups with weak order unit, that are not comparable with any known H-closed epireflections of W other than the divisible hull and the epicompletion. In preparation, we show that the free objects in any Hclosed epireflective subcategory of W must be closed under composition (see section 2 for a precise d...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1970
ISSN: 0002-9947
DOI: 10.2307/1995415