Intersection properties of stable subgroups and bounded cohomology. (English) Zbl 1472.20088
Summary: We show that a finite collection of stable subgroups of a finitely generated group has finite height, finite width, and bounded packing. We then use knowledge about intersections of conjugates to characterize finite families of quasimorphisms on hyperbolically embedded subgroups that can be simultaneously extended to the ambient group.
MSC:
| 20F67 | Hyperbolic groups and nonpositively curved groups |
| 20F65 | Geometric group theory |
| 20J06 | Cohomology of groups |
| 20F05 | Generators, relations, and presentations of groups |
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