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Title: Polycyclic-by-finite groups admit a polynomial structure of bounded degree
Authors: Dekimpe, Karel * ×
Igodt, Paul G. * #
Issue Date: Feb-1997
Publisher: Gauthier-Villars
Series Title: Comptes Rendus de l'Académie des Sciences. Série I, Mathématique vol:324 issue:3 pages:303-306
Abstract: We know, from recent examples given by Benoist, Burde and Grunewald, that there exist polycyclic-by-finite groups Gamma, of rank h (the examples given were in fact nilpotent), admitting no properly discontinuous affine action on R-h. On the other hand for such Gamma's, it is always possible to construct a properly discontinuous smooth action of Gamma on R-h. Our main result is that any polycyclic-by-finite group Gamma of rank h acts properly discontinuously and by polynomial diffeomorphisms of bounded degree on R-h. This result follows from an unexpected and deep cohomology vanishing theorem. In this way, the best possible general answer to a question of John Milnor is probably given.
URI: 
ISSN: 0764-4442
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Mathematics, Campus Kulak Kortrijk
* (joint) first author
× corresponding author
# (joint) last author

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