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On the Residual Finiteness of Certain Mapping Class Groups
Author(s) -
Grossman Edna K.
Publication year - 1974
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-9.1.160
Subject(s) - modulo , mathematics , interpretation (philosophy) , class (philosophy) , genus , group (periodic table) , surface (topology) , residual , algebraic number , identity (music) , mapping class group , pure mathematics , combinatorics , physics , geometry , computer science , mathematical analysis , biology , algorithm , artificial intelligence , zoology , quantum mechanics , acoustics , programming language
Let T k be a compact orientable surface of genus k . By the mapping class group, M ( T k ), of T k we mean the group of all orientation‐preserving homeomorphisms of T k k modulo those isotopic to the identity. We prove here that M ( T k ) is residually finite, using the algebraic interpretation of M ( T k ) due to Nielsen.