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Jan 15 at 3:12 comment added mathreader I'll record here another useful article that is relevant to the topic:$\tag*{}$ Søren Kjærgaard Boldsen, Different versions of mapping class groups of surfaces arxiv.org/abs/0908.2221
Feb 7, 2021 at 15:39 comment added Allen Hatcher This paper uses the definition of the mapping class group as homotopy classes of homeomorphisms (or diffeomorphisms) rather than isotopy classes. Injectivity is fairly easy with this definition. More work is needed to get injectivity for isotopy classes.
Feb 7, 2021 at 7:38 history answered mathreader CC BY-SA 4.0