2022-08-08T22:34:00Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000056512021-03-01T16:25:25Z2次元円板の面積保存微分同相群上の擬準同型Quasi-morphisms on the group of area-preserving diffeomorphisms of the 2-diskIshida, Tomohiko11752University of Tokyo (東京大学)博士(数理科学)Recently Gambaudo and Ghys proved that there exist infinitely many quasi-morphisms on the group ${\rm Diff}_\Omega^\infty (D^2, \partial D^2)$ of area-preserving diffeomorphisms of the 2-disk $D^2$. For the proof, they constructed a homomorphism from the space of quasi-morphisms on the braid group to the space of quasi-morphisms on ${\rm Diff}_\Omega^\infty (D^2, \partial D^2)$. In this paper, we study this homomorphism and prove its injectivity. We give several applications of our result to stable commutator length of some element of ${\rm Diff}_\Omega^\infty (D^2, \partial D^2)$ and conjugation-invariant norms on ${\rm Diff}_\Omega^\infty (D^2, \partial D^2)$.thesis2013-03-252013-03-25application/pdfapplication/pdfhttps://repository.dl.itc.u-tokyo.ac.jp/record/5651/files/IshidaT_25_3_PhD_a.pdfhttps://repository.dl.itc.u-tokyo.ac.jp/record/5651/files/IshidaT_25_3_PhD_b.pdfeng