Ma 192c Introduction to 4-dimensional topology, Spring 2010
Day/Time: Tuesdays and Thursdays 14:30--15:55
Location: 257 Sloan
Office hours: Wednesdays 13:00--14:00 (office 251 Sloan)
Instructor: Yi Ni
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Course information
Prerequisite
Ma 151 and Ma 157a, or permission of the instructor.
Description
Since the breakthrough of Donaldson, the study of smooth 4-manifolds has been an active field in mathematics. This topic itself is fascinating. Great success has been achieved, but a lot of fundamental problems are still widely open. Moreover, four-dimensional topology has close relationships with other fields in low-dimensional topology like knot theory, mapping class groups and 3-manifolds, as well as connections with complex, symplectic and algebraic geometry. In this course, we will discuss some basic facts about 4-dimensional topology. The plan is as follows.
Introduction
Intersection forms
Complex and symplectic geometry in real dimension 4
Kirby calculus
Properties of Seiberg-Witten invariants, exotic 4-manifolds
Seiberg-Witten equations, Bauer-Furuta invariants, Taubes' Theorem
Textbook
Gompf, Robert E.; Stipsicz, Andras I. 4-manifolds and Kirby calculus. Graduate Studies in Mathematics, 20. American Mathematical Society, Providence, RI, 1999. ISBN: 0-8218-0994-6.
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