\( \def\bbN{{\mathbb N}} \def\bbQ{{\mathbb Q}} \def\bbR{{\mathbb R}} \def\bbZ{{\mathbb Z}} \def\calA{{\mathcal A}} \def\calD{{\mathcal D}} \def\calT{{\mathcal T}} \def\Lim{{\operatorname{Lim}}} \) © | Dror Bar-Natan: Classes: 2025-26:

MAT1301S - Algebraic Topology

Toronto, Spring 2026

Agenda. Learn about the surprising relation between the easily deformed (topology) and the most rigid (algebra).

Ambition. Get to the Wirtinger presentation of the fundamental group of knot complements and to the definition of the Alexander polynomial as the order ideal of the first homology of the universal Abelian cover of a knot complement. Both of these goals are just a bit too far, yet they can serve as perfect motivators for all that isn't too far.

Instructor. Dror Bar-Natan, drorbn@math.toronto.edu (for course administration matters only; math on email is slow and prone to misunderstandings, so I generally avoid it). Office: Bahen 6178.


Charlie Wu

Teaching Assistant. Charlie Wu, charliec.wu@mail.utoronto.ca.

Classes. Mondays 10-11am and Tuesdays 4-6pm, at Bahen 6183.

Office Time. Wednesdays 2-3:30pm at Bahen 6178 and online at https://drorbn.net/vchat.

Text. Mostly Alan Hacther's Algebraic Topology, but also several specialized sources for specialized topics.

URL. https://drorbn.net/26-1301.

Course Calendar

# Week of ... Things
1 January 5-9 Handout: About This Class.
Tuesday/Wednesday: Homework Assignment 1 will likely be assigned.
2 January 12-16 Tuesday/Wednesday: Homework Assignment 2 will likely be assigned.
Wednesday: Dror's office time only 2:00-3:00.
3 January 19-24 Dror will be away this week and the class will most likely be taught by Alexander Kupers.
Tuesday: Today's class is at UC 256 (one time only).
Wednesday: No Dror's office time.
4 January 26-30 Tuesday: Class photo during break.
Tuesday/Wednesday: Homework Assignment 3 will likely be assigned.
Wednesday: Dror's office time only 2:00-3:00.
5 February 2-6 Thursday: our Term Test will likely take place at 6-8pm.
6 February 9-13 Tuesday/Wednesday: Homework Assignment 4 will likely be assigned.
R February 16-20 Monday is Family Day, and the week is Reading Week - no classes and no office time.
7 February 23-27 Tuesday/Wednesday: Homework Assignment 5 will likely be assigned.
Friday is the last date for graduate students to drop this class without penalty.
8 March 2-6 Tuesday/Wednesday: Homework Assignment 6 will likely be assigned.
9 March 9-13  
10 March 16-20 Tuesday/Wednesday: Homework Assignment 7 will likely be assigned.
11 March 23-27 Tuesday/Wednesday: Homework Assignment 8 will likely be assigned.
12 March 30 - April 3  
F April 6-10 I hope that our final examination will be scheduled for sometime this week.

Further resources: