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.

Logistics

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.

Exercises

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

Schedule

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