English

Gambaudo--Ghys construction on bounded cohomology

Geometric Topology 2024-05-03 v6 Group Theory

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.

Keywords

Cite

@article{arxiv.2009.00124,
  title  = {Gambaudo--Ghys construction on bounded cohomology},
  author = {Mitsuaki Kimura},
  journal= {arXiv preprint arXiv:2009.00124},
  year   = {2024}
}

Comments

Minor revision, 16 pages, 6 figures, to appear in Journal of the Mathematical Society of Japan