Geodesic
Isometries of systolic spaces
Tomasz Elsner1
1 Department of Mathematics The Ohio State University 231 W 18th Ave. Columbus, OH 43210, U.S.A. and Instytut Matematyczny Uniwersytet Wroc/lawski pl. Grunwaldzki 2//4 50-384 Wroc/law, Poland
Fundamenta Mathematicae, Tome 204 (2009) no. 1, pp. 39-55

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We provide a classification of isometries of systolic complexes corresponding to the classification of isometries of CAT(0)-spaces. We prove that any isometry of a systolic complex either fixes the barycentre of some simplex (elliptic case) or stabilizes a thick geodesic (hyperbolic case). This leads to an alternative proof of the fact that finitely generated abelian subgroups of systolic groups are undistorted.
DOI : 10.4064/fm204-1-3
Keywords: provide classification isometries systolic complexes corresponding classification isometries cat spaces prove isometry systolic complex either fixes barycentre simplex elliptic stabilizes thick geodesic hyperbolic leads alternative proof finitely generated abelian subgroups systolic groups undistorted

Tomasz Elsner 1

1 Department of Mathematics The Ohio State University 231 W 18th Ave. Columbus, OH 43210, U.S.A. and Instytut Matematyczny Uniwersytet Wroc/lawski pl. Grunwaldzki 2//4 50-384 Wroc/law, Poland 
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Tomasz Elsner. Isometries of systolic spaces. Fundamenta Mathematicae, Tome 204 (2009) no. 1, pp. 39-55. doi: 10.4064/fm204-1-3

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