Geodesic
On signatures and a subgroup of a central extension to the mapping class group
Homology, homotopy, and applications, Tome 5 (2003) no. 1, pp. 251-260.

Voir la notice de l'article provenant de la source International Press of Boston

Atiyah’s work [1] describes the relationship between multiplication in a central extension of the mapping class group of a surface of genus $n$ and the signatures of $4$-dimensional manifolds. This work studies a subgroup of the central extension, which comes from the image of a representation of the pure framed braid group on $n$-strands found in [5], and the signatures of corresponding $4$-manifolds via a split exact sequence. We construct a splitting map to prove the sequence is split exact, and we use the splitting to give a topological description of homology classes in $4$-dimensional manifolds with non-zero intersection. We conclude with a description of multiplication in the subgroup.
DOI : 10.4310/HHA.2003.v5.n1.a11
Classification : 20F36, 57M25, 57N05, 57N13
Keywords: mapping class group, pure braids, signatures 
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Jonathan Natov. On signatures and a subgroup of a central extension to the mapping class group. Homology, homotopy, and applications, Tome 5 (2003) no. 1, pp. 251-260. doi : 10.4310/HHA.2003.v5.n1.a11. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2003.v5.n1.a11/

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