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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
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.
You need to know some symplectic geometry and some complex geometry.
Tuesday 2pm-3pm (P143)
Tuesday 3pm-4pm (Math 4-101B).
Wednesday 11am-12pm (Math 4-101B)
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