We simplify and generalize McDuff’s construction of symplectic 4-manifolds with disconnected boundary of contact type in terms of the linking pairing defined on the dual of 3-dimensional Lie algebras. This leads us to an observation that an Anosov flow gives rise to a bi-contact structure, i.e. a transverse pair of contact structures with different orientations, and the construction turns out to work for 3-manifolds which admit Anosov flows with smooth invariant volume. Finally, new examples of bi-contact structures are given and related dynamical problems around bi-contact structures are raised.
La construction par McDuff de variétés symplectiques de dimension 4 à bord non connexe de type contact, est simplifiée et généralisée en termes du produit scalaire d’enlacement sur le dual des algèbres de Lie de dimension 3. Cela nous amène à observer que les flots d’Anosov donnent des structures de bi-contact, c’est-à-dire une paire transversale de structures de contact avec orientations opposées. De plus, on voit que la construction se généralise aux variétés de dimension 3 qui admettent un flot d’Anosov avec un volume invariant lisse. Enfin, de nouveaux exemples de structure de bi-contact sont donnés et les problèmes dynamiques autour des structures de bi-contact sont proposés.
@article{AIF_1995__45_5_1407_0, author = {Mitsumatsu, Yoshihiko}, title = {Anosov flows and {non-Stein} symplectic manifolds}, journal = {Annales de l'Institut Fourier}, pages = {1407--1421}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {45}, number = {5}, year = {1995}, doi = {10.5802/aif.1500}, mrnumber = {96m:53029}, zbl = {0834.53031}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1500/} }
TY - JOUR AU - Mitsumatsu, Yoshihiko TI - Anosov flows and non-Stein symplectic manifolds JO - Annales de l'Institut Fourier PY - 1995 SP - 1407 EP - 1421 VL - 45 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1500/ DO - 10.5802/aif.1500 LA - en ID - AIF_1995__45_5_1407_0 ER -
%0 Journal Article %A Mitsumatsu, Yoshihiko %T Anosov flows and non-Stein symplectic manifolds %J Annales de l'Institut Fourier %D 1995 %P 1407-1421 %V 45 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1500/ %R 10.5802/aif.1500 %G en %F AIF_1995__45_5_1407_0
Mitsumatsu, Yoshihiko. Anosov flows and non-Stein symplectic manifolds. Annales de l'Institut Fourier, Volume 45 (1995) no. 5, pp. 1407-1421. doi : 10.5802/aif.1500. http://archive.numdam.org/articles/10.5802/aif.1500/
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