no. 5
Anosov flows and non-Stein symplectic manifolds
Annales de l'Institut Fourier, Tome 45 (1995) no. 5, pp. 1407-1421

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.

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     author = {Mitsumatsu, Yoshihiko},
     title = {Anosov flows and {non-Stein} symplectic manifolds},
     journal = {Annales de l'Institut Fourier},
     pages = {1407--1421},
     year = {1995},
     publisher = {Association des Annales de l'Institut Fourier},
     volume = {45},
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Mitsumatsu, Yoshihiko. Anosov flows and non-Stein symplectic manifolds. Annales de l'Institut Fourier, Tome 45 (1995) no. 5, pp. 1407-1421. doi: 10.5802/aif.1500

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