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