MAS435 Algebraic Topology




Course outline

This is provided in Chapter 1 of the notes.

Lecture Notes

Currently available Chapters 1-2 , Chapters 3-4 , Chapters 5-6 , Chapters 7-9 , Chapters 10-11 , Chapters 12-13 , Chapters 14-15 (Chapters 1-9 should be stable, but there may be minor amendments from Chapter 10 onwards). Later chapters will be uploaded as the course progresses.
The plan for Semester 1 is as follows.
Chapter 1: Introduction and motivation. What is algebraic topology?
Chapter 2: Topological spaces
Chapter 3: A little general topology
Chapter 4: Path components
Chapter 5: Homotopy and homotopy equivalence
Chapter 6: The fundamental group
Chapter 7: The fundamental group of the circle and covering spaces.
Chapter 8: The Seifert-van Kampen theorem.
Chapter 9: Group actions and the fundamental group.
The plan for Semester 2 is as follows.
Chapter 10: Simplicial complexes.
Chapter 11: Homology.
Chapter 12: Homology of simplicial complexes
Chapter 13: Chain homotopy, cones and spheres.
Chapter 14: The Mayer-Vietoris sequence.
Chapter 15: The simplicial approximation theorem.
Chapter 16: Topological invariance of simplicial homology
An alternative route, not planned for this year would include
Chapter 17: The Euler characteristic and the Lefschetz Fixed Point Theorem.

Problem sheets and assignments

Semester 2 Problems for weekly practice (new problem each week) .pdf will be uploaded as the course progresses (contributes to assessment)
Problems from Semester 1.
Other exercise sheets will be added intermittently.
Exercises 1 (.pdf)
Exercises 2 (.pdf)

Semester 1 Solutions

Added at the appropriate time. Solutions to Weekly Exercises for Week 1
Solutions to Weekly Exercises for Week 2
Solutions to Weekly Exercises for Week 3
Solutions to Weekly Exercises for Week 4
Solutions to Weekly Exercises for Week 5
Solutions to Weekly Exercises for Week 6
Solutions to Weekly Exercises for Week 8
Solutions to Weekly Exercises for Week 9
Solutions to Weekly Exercises for Week 10

Semester 2 Solutions

Solutions to Weekly Exercises for Week 1
Solutions to Weekly Exercises for Week 2
Solutions to Weekly Exercises for Week 3
Solutions to Weekly Exercises for Week 4
Solutions to Weekly Exercises for Week 5
Solutions to Weekly Exercises for Week 6

Past exams

Solutions to the 2015-16 exam
Solutions to the 2016-17 exam


Questions?

If you have any doubts or difficulties, you can email the lecturer, or make an appointment to discuss them:
N.P.Strickland@sheffield.ac.uk