Minimal displacement set for weakly systolic complexes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914939850981376 |
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| author | Lazar, Ioana-Claudia |
| author_facet | Lazar, Ioana-Claudia |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03850 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimal displacement set for weakly systolic complexes Lazar, Ioana-Claudia Group Theory Combinatorics Geometric Topology Metric Geometry 20F67, 05C99 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). |
| title | Minimal displacement set for weakly systolic complexes |
| topic | Group Theory Combinatorics Geometric Topology Metric Geometry 20F67, 05C99 |
| url | https://arxiv.org/abs/2409.03850 |