Back to Search
Start Over
7-location, weak systolicity and isoperimetry
- Publication Year :
- 2024
-
Abstract
- $m$-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.<br />Comment: 15 pages, 10 figures
- Subjects :
- Mathematics - Combinatorics
Mathematics - Group Theory
20F65, 20F67
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2409.00612
- Document Type :
- Working Paper