Poisson Geometry and Its Applications

Special Session Speaker


Poisson structures on smooth 4-manifolds

Suárez-Serrato Pablo

In joint works with Garc{\'i}a-Naranjo, Vera [1], and Torres Orozco [2], we described the Poisson bivectors and computed the symplectic forms of Poisson structures associated to broken and wrinkled Lefschetz fibrations on closed oriented smooth 4-manifolds. Since these exist in every closed oriented smooth 4-manifold, this gives a new outlook on the geometry of smooth 4-manifolds. These Poisson structures are complete and if the genus of the fibers is at least one, then they are also integrable. Using these constructions we can give examples of countably many Poisson structures on a smooth 4-manifold that are pairwise Morita inequivalent. We have also extended these results to higher dimensions [3]. [1] L.C. Garc{\'i}a-Naranjo, P. Su{\'a}rez-Serrato, R. Vera, {\it Poisson structures on smooth 4-manifolds,} Lett. Math. Phys. 105 (2015), no. 11, 1533--1550. [2] P. Su{\'a}rez-Serrato, J. Torres Orozco, {\it Poisson structures on wrinkled fibrations,} Bol. Soc. Mat. Mex. (3) 22 (2016), no. 1, 263--280. [3] P. Su{\'a}rez-Serrato, J. Torres Orozco, R. Vera, {\it Poisson and near-symplectic structures on generalized wrinkled fibrations in dimension 6}, {\tt arXiv:1609.06768.}

Thursday August 17 , 17:30 - 16:10