Jonathan C. Johnson

Office: PMA 12.136
Department of Mathematics
University of Texas at Austin

Dehn Surgery and 3-Manifolds - 2019 Summer Mini-Course

This mini-course is an introduction to the basic properties of Dehn surgery on knots in 3-manifolds. Dehn surgery was first introduced by Dehn in 1910 as an alternative way to condtruct the Poincaré homology sphere. Since then Dehn surgery has played a important role in 3-manifold theory. The primary resource for this course will be the "Dehn Surgery and 3-Manifolds" notes from the 2016 Park City Mathematics Institute Graduate Summer School by Cameron Gordon. We will also refer to parts on Dale Rolfsen's Knots and Links and "Lectures on Heegaard Floer Homology" by Ozsváth and Szabó. The material should be accessible to anyone comfortable with algebraic topology and differential topology prelim material. Topics will include the cabling conjecture, the Berge conjecture and L-space surgeries.


Cameron Gordon, "Dehn Surgery and 3-Manifolds"
Ozsváth and Szabó, "Lectures on Heegaard Floer Homology"
Dale Rolfsen, Knots and Links
Allen Hatcher, Notes on 3-Manifolds


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


This course will meet in RLM 12.166. Here's the tentative schedule for this course.:

Monday - June 10

10:00-11:00am 3-Manifolds and Knots
3:00pm-whenever Exercise Session #1

Tuesday, June 11

10:00-11:00am Introduction to Dehn Surgery
3:00pm-whenever Exercise Session #2

Wednesday, June 12

10:00-11:00am Lens Space Surgeries
3:00pm-whenever Exercise Session #3

Thursday, June 13

10:00-11:00am Reducible Surgeries
3:00pm-whenever Exercise Session #4

Friday, June 14

10:00-11:00am L-Space Surgeries
3:00pm-whenever Exercise Session #5