Certain Gambaudo-Ghys and Polterovich quasimorphisms extend C^0-continuously to Homeo_0(M,μ) as quasimorphisms and to Homeo_0(M) as cochains with semi-bounded differentials, implying unbounded metrics on commutator subgroups and conditions for undistorted homeomorphisms.
Distortion elements of Diff∞ 0 (M).Bull
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On quasimorphisms and distortion in homeomorphism groups
Certain Gambaudo-Ghys and Polterovich quasimorphisms extend C^0-continuously to Homeo_0(M,μ) as quasimorphisms and to Homeo_0(M) as cochains with semi-bounded differentials, implying unbounded metrics on commutator subgroups and conditions for undistorted homeomorphisms.