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...
متن کاملGroups of piecewise projective homeomorphisms
I 1924, Banach and Tarski (1) accomplished a rather paradoxical feat. They proved that a solid ball can be decomposed into five pieces, which are then moved around and reassembled in such a way as to obtain two balls identical to the original one (1). This wellnigh miraculous duplication was based on Hausdorff’s (2) 1914 work. In his 1929 study of the Hausdorff–Banach–Tarski paradox, von Neuman...
متن کاملMather Invariants in Groups of Piecewise-linear Homeomorphisms
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 کاملConstructing Piecewise Linear Homeomorphisms of Simple Polygons
Let P and Q be simple polygons with vertex sets fp1; : : : ; png and fq1; : : :, qng, respectively. We present an algorithm to construct a piecewise linear homeomorphism between P and Qmapping each vertex pi 2 P to qi 2 Q by constructing isomorphic triangulations of P and Q. These isomorphic triangulations consist of O(M log n+n log2 n) triangles where M is the size of the optimal (minimum size...
متن کاملPiecewise Linear Homeomorphisms: The Scalar Case
The class of piecewise linear homeomorphisms (PLH) provides a convenient functional representation for many applications wherein an approximation to data is required that is invertible in closed form. In this paper we introduce the graph intersection (GI) algorithm for ”learning” piecewise linear scalar functions in two settings we term ”approximation” (where an ”oracle” outputs accurate functi...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1992
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1992-1094555-4