7-location, weak systolicity and isoperimetry
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915325919887360 |
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| author | Hoda, Nima Lazăr, Ioana-Claudia |
| author_facet | Hoda, Nima Lazăr, Ioana-Claudia |
| contents | $m$-location is a local combinatorial condition for flag simplicial complexes introduced by Osajda. Osajda showed that simply connected 8-located locally 5-large complexes are hyperbolic. We treat the nonpositive curvature case of 7-located locally 5-large complexes.
We show that any minimal area disc diagram in a 7-located locally 5-large complex is itself 7-located and locally 5-large. We define a natural CAT(0) metric for 7-located disc diagrams and use this to prove that simply connected 7-located locally 5-large complexes have quadratic isoperimetric function. Along the way, we prove that locally weakly systolic complexes are 7-located locally 5-large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00612 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 7-location, weak systolicity and isoperimetry Hoda, Nima Lazăr, Ioana-Claudia Combinatorics Group Theory 20F65, 20F67 $m$-location is a local combinatorial condition for flag simplicial complexes introduced by Osajda. Osajda showed that simply connected 8-located locally 5-large complexes are hyperbolic. We treat the nonpositive curvature case of 7-located locally 5-large complexes. We show that any minimal area disc diagram in a 7-located locally 5-large complex is itself 7-located and locally 5-large. We define a natural CAT(0) metric for 7-located disc diagrams and use this to prove that simply connected 7-located locally 5-large complexes have quadratic isoperimetric function. Along the way, we prove that locally weakly systolic complexes are 7-located locally 5-large. |
| title | 7-location, weak systolicity and isoperimetry |
| topic | Combinatorics Group Theory 20F65, 20F67 |
| url | https://arxiv.org/abs/2409.00612 |