Minimal displacement set for weakly systolic complexes

2024/09/05 by Lazar, Ioana-Claudia · 1 citation
#05C99 #20F67 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2409.03850

Abstract

We investigate the structure of the minimal displacement set in weakly systolic complexes. We show that such set is systolic and that it embeds isometrically into the complex. As corollaries, we prove that any isometry of a weakly systolic complex either fixes the barycentre of some simplex (elliptic case) or it stabilizes a thick geodesic (hyperbolic case).

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• Minimal displacement set for CAT(0) cubical complexes

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