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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-1-3,
author = {Tomasz Elsner},
title = {Isometries of systolic spaces},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {39-55},
zbl = {1231.20037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-1-3}
}
Tomasz Elsner. Isometries of systolic spaces. Fundamenta Mathematicae, Tome 205 (2009) pp. 39-55. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-1-3/