Jonathan C. Johnson

Office: MSCS 524
Department of Mathematics
Oklahoma State University

Heegaard Splittings and Dehn Surgery - 2020 Summer Mini-Course

This mini-course covers some standard topics in 3-manifold topology including Heegaard splittings, the mapping class groups of closed surfaces, Seifert fibered spaces and Dehn surgery. This course will closely follow lectures 1 and 2 of Saveliev's Lectures on the Topology of 3-Manifolds, 2nd Edition. This course will be followed by the Kirby Calculus and 4-Manifolds mini-course covering lectures 3, 5, and 6. The glossary at the beginning of Saveliev's book is a good list of prerequisite topics. However, this course should be accessible to anyone comfortable with algebraic topology and differential topology preliminary material.


This course is part of the 2020 UT Summer Mini-Course series. Lectures and exercise sessions for this course will be held on Zoom. Lectures will be recorded and posted below in the schedule. If you would like to join the slack channel for this course, send me an e-mail.


Exercise Set #1
Exercise Set #2
Exercise Set #3
Exercise Set #4
Exercise Set #5


Here's the tentative schedule for this course. All times are in Central Daylight Time (GMT-5):

Monday - July 20

10:00-11:00am Sections 1.1-1.3: Introduction to Heegaard Splittings
2:00pm-4:00pm Exercise Session #1

Tuesday, July 21

10:00-11:00am Sections 1.4,1.5,1.7: Mapping Class Groups, Lens Spaces and Heegaard Diagrams
2:00pm-4:00pm Exercise Session #2

Wednesday, July 22

10:00-11:00am Sections 2.1-2.3: Dehn Surgery on Links
2:00pm-4:00pm Exercise Session #3

Thursday, July 23

10:00-11:00am Sections 2.3,1.6: Surgery Descriptions and Seifert Manifolds
2:00pm-4:00pm Exercise Session #4

Friday, July 24

10:00-11:00am Sections 7.1, 7.5, 7.6: Seifert Surfaces
2:00pm-4:00pm Exercise Session #5