Jonathan C. Johnson

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

Kirby Calculus and 4-Manifolds - 2020 Summer Mini-Course

This mini-course covers some standard topics in 4-manifold topology including Kirby calculus, intersection forms, Seifert homology spheres and the Rohlin invariant. This course will closely follow lectures 3, 5 and 6 of Saveliev's Lectures on the Topology of 3-Manifolds, 2nd Edition. This course will be preceded by the Heegaard Splittings and Dehn Surgery mini-course covering lectures 1 and 2. However, you are welcome to attend this course even if you did not attend the previous mini-course. The glossary at the beginning of Saveliev's book is a good list of prerequisite topics. However, this course should be accessible to anyone familiar with the basic concepts of Dehn surgery and 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 27

10:00-11:00am Sections 3.1, 3.2, 3.3: Framings and Rolfsen twist
2:00pm-4:00pm Exercise Session #1

Tuesday, July 28

10:00-11:00am Sections 3.2-3.4: Handle Decompositions and Kirby Diagrams
2:00pm-4:00pm Exercise Session #2

Wednesday, July 29

10:00-11:00am Sections 5.1-5.3: Intersection Forms
2:00pm-4:00pm Exercise Session #3

Thursday, July 30

10:00-11:00am Sections 2.4, 6.1: 4-Manifolds with Boundary
2:00pm-4:00pm Exercise Session #4

Friday, July 31

10:00-11:00am Sections 6.2-6.4: Seifert Homology Spheres and the Rohlin Invariant
2:00pm-4:00pm Exercise Session #5