Automorphism Subgroups of Finite Index in Algebraic Mapping Class Groups

Warren Dicks, Edward Formanek

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

We give an algebraic proof of the Birman-Bers theorem - an algebraic result whose previous proofs used topology or analysis, and which says that a certain subgroup of finite index in the (algebraic) mapping class group of an oriented punctured surface is isomorphic to a certain group of automorphisms. The index 2 case gives rise to an automorphism of the group consisting of those automorphisms of a free group that stabilize the normal subgroup generated by an oriented-surface relator, and we analyze this curious automorphism. © 1997 Academic Press.
Original languageEnglish
Pages (from-to)58-89
JournalJournal of Algebra
Volume189
DOIs
Publication statusPublished - 1 Mar 1997

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