# Topology II: Algebraic topology

## Course information

• Code: MAT1301HF
• Instructor: Marco Gualtieri, office hours by appointment.
• Class schedule: R10-11:30 and F2-3:30
• Schedule changes:
• Teaching assistant: Peter Crooks
• Evaluation: The final grade is $$\tfrac{a}{2} + \tfrac{t}{4} + \tfrac{f}{4},$$ where $$a$$ is the average of the four best assignment grades, $$t$$ is the term exam grade, and $$f$$ is the final exam grade, all out of 100.
• Qualifying exam: If the average of your grades from MAT1300F and MAT1301S is at least A-, you will be exempt from the Topology qualifying exam.
• Term Exam: March 1, in class.
• Final Exam:

## Assignments

Please discuss the problems, but avoid reading a written solution before you write your own, since these must be original.

Late assignments are not be accepted: please hand in whatever you have at the deadline.

Assignments are marked for correctness, but also clarity. Keep your solutions concise, and make sure the structure of your argument is clear. I suggest that you type out your solutions in LaTeX.

Finally, the no B.S. bonus provides a 10% bonus for an assignment with no false statements.

• Assignment 1 (tex) (pdf) Due date: January 31, 2013.
• Assignment 2 (tex) (pdf) Due date (revised): March 1, 2013.
• Assignment 3 (tex) (pdf) Due date: March 14, 2013.
• Assignment 4 (tex) (pdf) Due date: March 22, 2013 (remove Ex. 1, #10).
• Assignment 5 (tex) (pdf) Due date: April 8, 2013.

## Overview of topics

The fundamental group and groupoid. Covering spaces. Van-Kampen's theorem. Simplicial homology and the Cartan–Eilenberg axioms. Cellular homology. Subdivision and excision. Cohomology. Beginnings of homological algebra.

## Suggested references

The main reference is Hatcher. Notes will also be provided. Another great resource is Bredon's "Topology and Geometry". Of course, also Bott & Tu.