The second Johnson homomorphism and the second rational cohomology of the Johnson kernel

• Autores: Takuya Sakasai
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 143, Nº 3, 2007, págs. 627-648
• Idioma: inglés
• DOI: 10.1017/s0305004107000564
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• Resumen

  • The Johnson kernel is the subgroup of the mapping class group of a surface generated by Dehn twists along bounding simple closed curves, and has the second Johnson homomorphism as a free abelian quotient. In terms of the representation theory of the symplectic group, we give a complete description of cup products of two classes in the first rational cohomology of the Johnson kernel obtained by the rational dual of the second Johnson homomorphism.