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.
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
@article{AIF_2015__65_6_2711_0, author = {Kawazumi, Nariya and Kuno, Yusuke}, title = {Intersection of curves on surfaces and their applications to mapping class groups}, journal = {Annales de l'Institut Fourier}, pages = {2711--2762}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {65}, number = {6}, year = {2015}, doi = {10.5802/aif.3001}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.3001/} }
TY - JOUR AU - Kawazumi, Nariya AU - Kuno, Yusuke TI - Intersection of curves on surfaces and their applications to mapping class groups JO - Annales de l'Institut Fourier PY - 2015 SP - 2711 EP - 2762 VL - 65 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.3001/ DO - 10.5802/aif.3001 LA - en ID - AIF_2015__65_6_2711_0 ER -
%0 Journal Article %A Kawazumi, Nariya %A Kuno, Yusuke %T Intersection of curves on surfaces and their applications to mapping class groups %J Annales de l'Institut Fourier %D 2015 %P 2711-2762 %V 65 %N 6 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.3001/ %R 10.5802/aif.3001 %G en %F AIF_2015__65_6_2711_0
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. http://archive.numdam.org/articles/10.5802/aif.3001/
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