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Reeb Dynamics of Lens Spaces
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From the Columbia Mathematics Summer 2014 Undergraduate Research Project.
The lens space L(n+1,n) is obtained as the quotient of S^3 by the cyclic subgroup Z_{n+1} of SU_2(C). We can also view this lens space as the link of a hypersurface singularity M:=f^{-1}(0) \cap S^5 in C^3, where f(z_0,z_1,z_2)=z_0^{n+1}+z_1^2+z_2^2. This talk will explain some contact geometric properties of M. We will introduce the notion of a contact structure and see how it gives rise to a globally defined vector field, known as the Reeb vector field. Using M as the model of the lens space we will explain some particular dynamics of the Reeb vector field that we studied this summer.
Leonardo Abbrescia, Willie Dong, Irit Huq-Kuruvilla, and Nawaz Sultani
(advised by Jo Nelson and Robert Castellano)
The lens space L(n+1,n) is obtained as the quotient of S^3 by the cyclic subgroup Z_{n+1} of SU_2(C). We can also view this lens space as the link of a hypersurface singularity M:=f^{-1}(0) \cap S^5 in C^3, where f(z_0,z_1,z_2)=z_0^{n+1}+z_1^2+z_2^2. This talk will explain some contact geometric properties of M. We will introduce the notion of a contact structure and see how it gives rise to a globally defined vector field, known as the Reeb vector field. Using M as the model of the lens space we will explain some particular dynamics of the Reeb vector field that we studied this summer.
Leonardo Abbrescia, Willie Dong, Irit Huq-Kuruvilla, and Nawaz Sultani
(advised by Jo Nelson and Robert Castellano)