Abstract
Let be a group, a hyperbolically embedded subgroup of , a normed –module, an –invariant submodule of . We propose a general construction which allows to extend –quasicocycles on with values in to –quasicocycles on with values in . As an application, we show that every group with a nondegenerate hyperbolically embedded subgroup has for . This covers many previously known results in a uniform way. Applying our extension to quasimorphisms and using Bavard duality, we also show that hyperbolically embedded subgroups are undistorted with respect to the stable commutator length.
Citation
Michael Hull. Denis Osin. "Induced quasicocycles on groups with hyperbolically embedded subgroups." Algebr. Geom. Topol. 13 (5) 2635 - 2665, 2013. https://doi.org/10.2140/agt.2013.13.2635
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