Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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THE ACTION OF IMAGE OF BRAIDING UNDER THE HARER MAP

  • Published : 2006.04.01
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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.

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References

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  1. THE BRAIDINGS IN THE MAPPING CLASS GROUPS OF SURFACES vol.50, pp.4, 2013, https://doi.org/10.4134/JKMS.2013.50.4.865