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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 Elsner. "Isometries of systolic spaces." Fundamenta Mathematicae 204.1 (2009): 39-55. <http://eudml.org/doc/282729>.
@article{TomaszElsner2009, abstract = {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.}, author = {Tomasz Elsner}, journal = {Fundamenta Mathematicae}, keywords = {systolic complexes; systolic groups; minimal surfaces; elliptic isometries; hyperbolic isometries; CAT(0)-spaces}, language = {eng}, number = {1}, pages = {39-55}, title = {Isometries of systolic spaces}, url = {http://eudml.org/doc/282729}, volume = {204}, year = {2009}, }
TY - JOUR AU - Tomasz Elsner TI - Isometries of systolic spaces JO - Fundamenta Mathematicae PY - 2009 VL - 204 IS - 1 SP - 39 EP - 55 AB - 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. LA - eng KW - systolic complexes; systolic groups; minimal surfaces; elliptic isometries; hyperbolic isometries; CAT(0)-spaces UR - http://eudml.org/doc/282729 ER -