Intersection of curves on surfaces and their applications to mapping class groups

Kawazumi, Nariya; Kuno, Yusuke

Annales de l'Institut Fourier, Tome 65 (2015) no. 6, pp. 2711-2762.

Nous introduisons une opération qui mesure l’auto-intersection des chemins sur une surface orientée. Comme applications, nous donnons un critère de la réalisabilité d’un twist de Dehn généralisé, et nous obtenons une contrainte géométrique sur l’image des homomorphismes de Johnson.

We introduce an operation which measures the self intersections of paths on an oriented surface. As applications, we give a criterion of the realizability of a generalized Dehn twist, and derive a geometric constraint on the image of the Johnson homomorphisms.

Classification : 57N05, 20F34, 32G15
Keywords: Goldman bracket, Turaev cobracket, Lie bialgebra, mapping class group, Dehn twist, Johnson homomorphisms
Mot clés : crochet de Goldman, co-crochet de Turaev, bigèbre de Lie, groupe de difféotopies, twist de Dehn, homomorphismes de Johnson

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