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Groups of PL homeomorphisms of cubes
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 5, pp. 1261-1292.

We study algebraic properties of groups of PL or smooth homeomorphisms of unit cubes in any dimension, fixed pointwise on the boundary, and more generally PL or smooth groups acting on manifolds and fixing pointwise a submanifold of codimension 1 (resp. codimension 2), and show that such groups are locally indicable (resp. circularly orderable). We also give many examples of interesting groups that can act, and discuss some other algebraic constraints that such groups must satisfy, including the fact that a group of PL homeomorphisms of the n-cube (fixed pointwise on the boundary) contains no elements that are more than exponentially distorted.

Nous étudions les propriétés algébriques de groupes des homéomorphismes PL ou lisses des cubes unitaires dans toutes les dimensions, point par point fixe sur la frontière, et des groupes plus généralement PL ou lisses agissant sur les variétés et qui fixe ponctuellement une sous-variété de codimension 1 (resp. codimension 2), et montrent que ces groupes sont localement indicables (resp. de circulairement ordonnable). Nous donnons également de nombreux exemples de groupes intéressants qui peuvent agir, et discutons de certaines autres contraintes algébriques que ces groupes doivent satisfaire, y compris le fait qu’un groupe d’homéomorphismes PL de la n-cube (ponctuelle fixe sur la frontière) ne contient pas éléments qui soient plus qu’exponentiellement distordus.

DOI: 10.5802/afst.1484
Danny Calegari 1; Dale Rolfsen 2

1 Department of Mathematics, University of Chicago, Chicago, IL 60637, USA
2 Department of Mathematics, University of British Columbia, Vancouver, Canada
     author = {Danny Calegari and Dale Rolfsen},
     title = {Groups of {PL} homeomorphisms of cubes},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {1261--1292},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 24},
     number = {5},
     year = {2015},
     doi = {10.5802/afst.1484},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1484/}
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Danny Calegari; Dale Rolfsen. Groups of PL homeomorphisms of cubes. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 5, pp. 1261-1292. doi : 10.5802/afst.1484. https://afst.centre-mersenne.org/articles/10.5802/afst.1484/

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