Course outlineThis is provided in Chapter 1 of the notes.Lecture NotesCurrently 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 assignmentsSemester 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 SolutionsAdded at the appropriate time. Solutions to Weekly Exercises for Week 1Solutions 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 SolutionsSolutions to Weekly Exercises for Week 1Solutions 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 examsSolutions to the 2015-16 examSolutions 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 |