Gambaudo--Ghys construction on bounded cohomology
Abstract
We consider a generalized Gambaudo--Ghys construction on bounded cohomology and prove its injectivity. As a corollary, we prove that the third bounded cohomology of the group of area-preserving diffeomorphisms on the 2-disk is infinite-dimensional. We also prove similar results for the case of the 2-sphere, the 2-torus and the annulus.
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