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Automorphism Subgroups of Finite Index in Algebraic Mapping Class Groups

✍ Scribed by Warren Dicks; Edward Formanek

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 316 KB
Volume: 189
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.6876

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✦ Synopsis

We give an algebraic proof of the Birman᎐Bers theoremᎏan algebraic result whose previous proofs used topology or analysis, and which says that a certain Ž . 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.

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