Intersection of curves on surfaces and their applications to mapping class groups
Annales de l'Institut Fourier, Volume 65 (2015) no. 6, pp. 2711-2762.

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.

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.

DOI: 10.5802/aif.3001
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
Kawazumi, Nariya 1; Kuno, Yusuke 2

1 University of Tokyo Department of Mathematical Sciences 3-8-1 Komaba Meguro-ku Tokyo 153-8914 (Japan)
2 Tsuda College Department of Mathematics 2-1-1 Tsuda-Machi, Kodaira-shi Tokyo 187-8577 (Japan)
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Kawazumi, Nariya; Kuno, Yusuke. Intersection of curves on surfaces and their applications to mapping class groups. Annales de l'Institut Fourier, Volume 65 (2015) no. 6, pp. 2711-2762. doi : 10.5802/aif.3001. https://aif.centre-mersenne.org/articles/10.5802/aif.3001/

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