Fall 2020

Instructor: John Baldwin

Email: john.baldwin@bc.edu

Office: Maloney 254

Office Hours: By appointment

Course time: M 2-3 and W 2-3:30

Zoom: Link. Meeting ID: 994 8554 5861. Email me for password.

Problem Session: I'll intersperse exercises throughout the lectures. Gage has generously offered to coordinate a weekly meeting to discuss course material and answer problems posed during class. It will meet on Fridays from 2-3. The Zoom link for the meeting is here. Meeting ID: 944 7811 2933. Same password as for course.

Course Description: This course is an introduction to several concepts of interest in the corner of low-dimensional topology I like to inhabit. We will start with basics of Heegaard splittings, Dehn surgery, 4-manifolds and Kirby calculus, and some knot theory, before moving to what I consider to be the meat of the course: the Rokhlin and Casson invariants, and applications thereof. I envision the latter material as a precursor to and motivation for instanton gauge theory, the subject of a future course. We will be guided to a large extent by Saveliev's beautiful book, "Lectures on the Topology of 3-Manifolds".

Other Resources: For a more comprehensive discussion of the Roklin and Casson invariants and their relationships with Floer homology, I recommend Saveliev's other book, "Invariants for Homology 3-Spheres". Other terrific books on nearby subjects include Gompf and Stipsicz's "4-Manifolds and Kirby Calculus" and Ozbagci and Stipsicz's "Contact 3-Manifolds and Stein Surfaces".

Class videos and notes:

• 9/2: vid, notes

• 9/9: vid, notes

• 9/14: vid, notes

• 9/16: vid, notes

• 9/21: vid, notes

• 9/23: vid, notes

• 9/28: vid, notes

• 9/30: vid, notes

• 10/5: vid, notes

• 10/7: vid, notes

• 10/13: vid,

• 10/14: vid, notes

• 10/19: vid, notes

• 10/21: vid, notes

• 10/26: vid,

• 10/28: vid,

• 11/2: vid,

• 11/4: vid,

• 11/9: vid,

• 11/11: vid,

• 11/16: vid,

• 11/18: vid,

• 11/23: vid,

• 11/30: vid,

• 12/2: vid,

• 12/7: vid,

• 12/9: vid,