MAS435 Algebraic Topology




Office Hour

Tuesday 13.00-14.00, J15 Hicks

Course outline

Look at Chapter 1 of the notes.

Lecture Notes

Currently Chapters 1-4 , Chapters 5-6 , Chapter 7-9 , Chapter 10-11 , Chapter 12-13 , Chapter 14-15 and Chapter 16-17 are all available. There may be some revisions to the later chapters as we cover them in lectures.
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.
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 Lefschetz Fixed Point Theorem
Chapter 16: The Simplicial Approximation Theorem.
Chapter 17: Topological Invariance of Homology (not examinable).

Problem sheets and assignments

Semester 1 problems for weekly practice (contribute to assessment) (.pdf)
Semester 2 problems for weekly practice (contribute to assessment) [new problem added each week] (.pdf)
Exercises 1 (.pdf)
Exercises 2 (.pdf)
Exercises 3 (.pdf)

Semester 1 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
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
Solutions to Weekly Exercises for Week 7

Past exams

Solutions to last year's exam (i.e., 2015-16) coming later.
Prior to that the syllabus was slightly different. Effects of the syllabus changes (which old exam questions are not relevant to the syllabus since 2015-16.) (.pdf)
2013-14 exam paper (.pdf)
2014-15 exam paper (.pdf)

Past exam solutions

2014-15 exam solutions.


Questions?

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

Escape routes


Last updated 11th March 2017.