Emmy Murphy in SGGTC
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Jen Hom
Apr 16, 2014, 10:48:36 AM4/16/14
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Hi folks,
Emmy Murphy will be speaking in the SGGTC on Friday at 10:45 am in 520 Math.
Title: Existence of overtwisted contact structures on high dimensional manifolds
Abstract: The Lutz-Martinet theorem states that any 2-plane field on a 3-manifold is homotopic to a contact structure. This construction lead to Eliashberg's definition of overtwisted contact manifolds, and in this context the existence theorem of Lutz-Martinet can be extended to a uniqueness result: any two overtwisted contact structures which are homotopic as plane fields are in fact isotopic. We discuss a recent extension of these results to contact manifolds of all dimensions. We will focus on showing that any almost contact structure is homotopic to a contact structure, and seeing how this leads to a new definition of overtwistedness in high dimensions. As time allows we will discuss a proof that a homotopy class of almost contact structures is realized by a unique isotopy class of overtwisted contact structure. This project is joint work with Borman and Eliashberg.
Best,
Emmy Murphy will be speaking in the SGGTC on Friday at 10:45 am in 520 Math.
Title: Existence of overtwisted contact structures on high dimensional manifolds
Abstract: The Lutz-Martinet theorem states that any 2-plane field on a 3-manifold is homotopic to a contact structure. This construction lead to Eliashberg's definition of overtwisted contact manifolds, and in this context the existence theorem of Lutz-Martinet can be extended to a uniqueness result: any two overtwisted contact structures which are homotopic as plane fields are in fact isotopic. We discuss a recent extension of these results to contact manifolds of all dimensions. We will focus on showing that any almost contact structure is homotopic to a contact structure, and seeing how this leads to a new definition of overtwistedness in high dimensions. As time allows we will discuss a proof that a homotopy class of almost contact structures is realized by a unique isotopy class of overtwisted contact structure. This project is joint work with Borman and Eliashberg.
Best,
Jen
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