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AUTOMORPHISMS OF BRAID GROUPS ON CLOSED SURFACES WHICH ARE NOT S², T², P² OR THE KLEIN BOTTLE

PING ZHANG

Department of Mathematics and Computer Science, Cankaya University, Ankara, Turkey

Department of Mathematics, Eastern Mediterranean University, North Cyprus

Current Affiliation with mailing address: Department of Mathematics, Eastern Mediterranean University, Gazimagusa, North Cyprus, via Mersin 10, Turkey.

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https://doi.org/10.1142/S0218216506005044Cited by:3 (Source: Crossref)

Abstract

Consider a surface braid group of n strings as a subgroup of the isotopy group of homeomorphisms of the surface permuting n fixed distinguished points. Each automorphism of the surface braid group (respectively, of the special surface braid group) is shown to be a conjugate action on the braid group (respectively, on the special braid group) induced by a homeomorphism of the underlying surface if the closed surface, either orientable or non-orientable, is of negative Euler characteristic. In other words, the group of automorphisms of such a surface braid group is isomorphic to the extended mapping class group of the surface with n punctures, while the outer automorphism group of the surface braid group is isomorphic to the extended mapping class group of the closed surface itself.

Dedicated to Prof. Sun Yifeng for His 80th Birthday

Keywords:

AMSC: 57N05, 57M05, 20F28, 20F36

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