LOW-DIMENSIONAL TOPOLOGY 

SPRING 2020   *   MATH 783

 

Textbook

Lectures on the topology of 3-manifoldsSecond Edition, by Nikolai Saveliev, Walter de Gruyter, 2012

Course contents

This course is a study of various invariants of 3- and 4-dimensional manifolds and knots.  I will begin by covering some classical material, including Heegaard splittings, Dehn surgery, Kirby calculus, invariants of knots and links, and topology of 4-manifolds. Depending on the audience’s interests, I will either proceed with the Casson invariant, or choose a different topic, such a the Chern-Simons functional or instanton gauge theory. Throughout the course, I will employ a rather intuitive approach to emphasize ideas behind the constructions, without getting buried in techical details.

Prerequisites

The course only assumes familiarity with some algebraic topology, including the fundamental group, covering spaces, and basic homology theory, and with the basics of differential topology.

Homework

http://www.math.miami.edu/~saveliev/hwk783.html