Coarse Geometry of Extended Admissible Groups Explored
Published:Dec 31, 2025 11:07
•1 min read
•ArXiv
Analysis
This paper investigates the coarse geometric properties of extended admissible groups, a class of groups generalizing those found in 3-manifold groups. The research focuses on quasi-isometry invariance, large-scale nonpositive curvature, quasi-redirecting boundaries, divergence, and subgroup structure. The results extend existing knowledge and answer a previously posed question, contributing to the understanding of these groups' geometric behavior.
Key Takeaways
- •Extended admissible groups are studied from a coarse geometric perspective.
- •Quasi-isometry type is invariant under changes in gluing edge isomorphisms.
- •Large-scale nonpositive curvature is demonstrated under mild conditions.
- •The class of groups with well-defined quasi-redirecting boundaries is enlarged.
- •Divergence is computed, generalizing a result from 3-manifold groups.
- •Subgroup structure is investigated.
Reference
“The paper shows that changing the gluing edge isomorphisms does not affect the quasi-isometry type of these groups.”