This is a copy of the original webpage for this course, which I taught at MSU in 2018. All of the contact information below is out of date.

Math 996: Special Topics in Topology

Spring 2018

Instructor: Kristen Hendricks
Office: D320 Wells Hall
Office Hours: By (encouraged!) appointment.
E-Mail: hendricks at math .msu .edu

A printable copy of the syllabus is here.

Location and Time

MW 12:40-2:00 in C329.

Prerequisites

Math 961 or equivalent.

Assignments

Optional exercises will be interspersed throughout lecture, and typically consolidated into a homework sheet at the end of the week. Registered students are expected to regularly attend class and give an hour talk during the last three (or possibly four, depending on number of students) weeks of the course. We will schedule the talks shortly before spring break; you should come meet with me around that time to plan a topic.

Resources

Expository papers:
P. Ozsváth and Z. Szabó, An introduction to Heegaard Floer homology
P. Ozsváth and Z. Szabó, Lectures on Heegaard Floer homology
P. Ozsváth and Z. Szabó, Heegaard diagrams and holomorphic disks
R. Lipshitz, Heegaard Floer homologies
C. Manolescu, An introduction to knot Floer homology
D. McDuff, Floer theory and low-dimensional topology

The original papers on Heegaard Floer homology:
P. Ozsváth and Z. Szabó, Holomorphic disks and topological invariants for closed three-manifolds
P. Ozsváth and Z. Szabó, Holomorphic disks and three-manifold invariants: properties and applications

Other references:
V. Turaev Torsion invariants of spin^c structures on 3-manifolds

Some references on low-dimensional topology:
N. Saveliev, Lectures on the topology of 3-manifolds
D. Rolfsen, Knots and links
R. Gompf and A. Stipsicz, 4-manifolds and Kirby calculus
R. Lickorish, An introduction to knot theory

Other research papers referenced in class:
This list will appear as the term progresses.

Lecture Notes

Lecture 1

Lecture 2

Lecture 3

Lecture 4

Lecture 5

Lecture 6

Lecture 7

Lecture 8

Lecture 9

Lecture 10

Lecture 11

Lecture 12

Lecture 13

Lecture 14

Lecture 15

Lecture 16

Lecture 17

Lectures 18 and 19

Lectures 20 and 21

Lecture 22

Lecture 23

Lecture 24

Weekly Exercise Sheets

Week 1

Week 2

Week 3

Week 4

Weeks 5 and 6

Week 7

Week 8