Instructor: Prof. Ian Hambleton
Email: hambleton@mcmaster.ca

Course Dates: January 8th - April 8th, 2024
Mid-Semester Break: February 19th - 23rd, 2024
Lecture Times: Mondays & Thursdays | 10:30 AM - 12:00 PM (ET)
Office Hours: Mondays & Thursdays | 1:00 PM - 2:30 PM (ET)

Registration Fee: PSU Students - Free | Other Students - CAD$500

Capacity Limit: 30 students

Format: Hybrid synchronous delivery

• In-Person: Fields Institute (Room 210) on Mondays (10:30 - 12:00) & McMaster University (Hamilton Hall 312) on Thursdays (10:30 - 12:00)
• Online: via Zoom

Course Description

Manifolds, cohomology, cup products. Poincaré duality, vector bundles, characteristic classes, spectral sequences, group actions. Introduction to surgery theory. Applications to the topology of algebraic varieties.

Prerequisites: Senior undergraduate level preparation in Algebra (groups, rings, fields),  Analysis (metric spaces, continuity, compactness, convergence), and Topology (fundamental groups and covering spaces).

Course Assessment (to be confirmed): The course assessment will include evaluation of biweekly problem assignments, and a written project report together with an in-class presentation (if time permits).

Reading List (to be expanded):

1. “Algebraic Topology”, A. Hatcher, https://pi.math.cornell.edu/~hatcher/AT/ATpage.html. Available online (free) or in hard copy from Cambridge University Press.
2. “Algebraic Topology: A First Course”, M. J. Greenberg and J. R. Harper. Available through university libraries.
3. “A Basic Course in Algebraic Topology”, W.S. Massey. Springer GTM 127.Available through university libraries.