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 All of the contact information below is out of date.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
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Office: | D320 Wells Hall
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Office Hours: | By (encouraged!) appointment.
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E-Mail: | hendricks at math .msu .edu
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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