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.
A refinement of bounded cohomology
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The space of contractible simple loops of fixed area on compact oriented surfaces has infinite L^p-diameter under the action of area-preserving diffeomorphisms.
citing papers explorer
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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.
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The $L^p$-diameter of the space of contractible loops
The space of contractible simple loops of fixed area on compact oriented surfaces has infinite L^p-diameter under the action of area-preserving diffeomorphisms.