Normal subgroups of big mapping class groups
نویسندگان
چکیده
Let S S be a surface and let M o d left-parenthesis upper S comma K right-parenthesis"> Mod ( , K stretchy="false">) encoding="application/x-tex">\operatorname {Mod}(S,K) the mapping class group of permuting Cantor subset subset-of ⊂<!-- ⊂ encoding="application/x-tex">K \subset S . We prove two structure theorems for normal subgroups (Purity:) if has finite type, every subgroup either contains kernel forgetful map to , or it is ‘pure’ — i.e. fixes set pointwise. (Inertia:) any alttext="n"> n encoding="application/x-tex">n element Q"> Q encoding="application/x-tex">Q set, there from pure P PMod {PMod}(S,K) alttext="left-parenthesis Q encoding="application/x-tex">(S,Q) fixing If N"> N encoding="application/x-tex">N contained in its image N Subscript encoding="application/x-tex">N_Q likewise normal. characterize exactly which finite-type arise this way. Several applications numerous examples are also given.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2022
ISSN: ['2330-0000']
DOI: https://doi.org/10.1090/btran/108