MAT 620 Tuesday, Thursday 11:30am-12:50pm, Mathematics 4130

MAT 620:Topics in Topology: Stein Manifolds and Weinstein Manifolds

Course Instructor: Mark McLean

Tuesday, Thursday 11:30am-12:50pm, Mathematics 4130

Introduction to the Course

In this course we will explore the relationship between Stein geometry and symplectic geometry pointed out originally by Eliashberg and Gromov. A Stein manifold is a closed properly embedded complex submanifold of \C^N. One should think of this as the complex analytic analogue of a smooth affine variety. We will study certain natural deformation classes of these manifolds called Stein homotopy classes. In this course we will show that such a problem is equivalent to studying deformation classes of purely symplectic objects called Weinstein manifolds. We will also explain which almost complex manifolds are smoothly deformation equivalent to Stein manifolds. If there is time we will give examples of symplectically exotic Stein manifolds. We will be following the book From Stein to Weinstein and Back, Symplectic Geometry of Affine Complex Manifolds by Kai Cieliebak and Yakov Eliashberg. This is an advanced course.

Prerequisites

You need to know some symplectic geometry and some complex geometry.

Office Hours: Tuesday 2pm-3pm (P143) Tuesday 3pm-4pm (Math 4-101B). Wednesday 11am-12pm (Math 4-101B)

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