Isometries of systolic spaces

Volume 204 / 2009

Tomasz Elsner Fundamenta Mathematicae 204 (2009), 39-55 MSC: 20F65, 20F67. DOI: 10.4064/fm204-1-3


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.


  • Tomasz ElsnerDepartment of Mathematics
    The Ohio State University
    231 W 18th Ave.
    Columbus, OH 43210, U.S.A.
    Instytut Matematyczny
    Uniwersytet Wroc/lawski
    pl. Grunwaldzki 2//4
    50-384 Wroc/law, Poland

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