[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2006.21.2.337

THE ACTION OF IMAGE OF BRAIDING UNDER THE HARER MAP

Song Yong-Jin (Department of Mathematics Inha University)

Publication Information

Communications of the Korean Mathematical Society / v.21, no.2, 2006 , pp. 337-345 More about this Journal

Abstract

John Harer conjectured that the canonical map from braid group to mapping class group induces zero homology homomorphism. To prove the conjecture it suffices to show that this map preserves the first Araki-Kudo-Dyer-Lashof operation. To get information on this homology operation we need to investigate the image of braiding under the Harer map. The main result of this paper is to give both algebraic and geometric interpretations of the image of braiding under the Harer map. For this we need to calculate long chains of consecutive actions of Dehn twists on the fundamental group of surface.

Keywords

braid group; mapping class group; Harer conjecture; (r, s)-braiding; double loop space; actions of Dehn twists;

Citations & Related Records

Reference

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