Course 421 - Algebraic Topology

Lecture Notes for the Academic Year 2008-9

The following sets of notes are currently available online:

• Section 1: Topological Spaces [PDF]
• Section 2: Homotopies and the Fundamental Group [PDF]
• Section 3: Covering Maps and the Monodromy Theorem [PDF]
• Section 4: Covering Maps and Discontinous Group Actions [PDF]
• Section 5: Simplicial Complexes [PDF]
• Section 6: Simplicial Homology Groups [PDF]
• Section 7: Homology Calculations [PDF]
• Section 8: Modules [PDF]
• Section 9: Introduction to Homological Algebra [PDF]
• Section 10: Exact Sequences of Homology Groups [PDF]

Non-Examinable Material 2008-9

Candidates will not be examined on section 8 (Modules) in 2009.

Candidates will not be examined on subsections 4.5 to 4.7 (from Lemma 4.18 to Corollary 4.26).

Candidates will not be examined on subsection 10.3 (The Mayer-Vietoris Sequence)

Worked Solutions for some recent 421 Exam Papers

• Annual Exam 1999 [PDF] [PostScript]
• Annual Exam 2003 [PDF] [PostScript]
• Annual Exam 2005 [PDF] [PostScript]
• Annual Exam 2007 [PDF] [PostScript]
• Annual Exam 2009 [PDF] [PostScript]

Lecture Notes for the Academic Year 2002-3

The following lecture notes for the academic year 2002-3 are currently available:-

Michaelmas Term 2002

[DVI], [PDF], [PostScript]

Hilary Term 2003

[DVI], [PDF], [PostScript]

Problem Sets for the Academic Year 2002-3

The following problems sets for the academic year 2002-3 are currently available:-

Problems I

[DVI], [PDF], [PostScript]

Problems II

[PDF], [PostScript]

Lecture Notes for the Academic Year 1998-9

The lecture notes for course 421 (Algebraic topology), taught at Trinity College, Dublin, in the academic year 1998-1999, are available also here. (Note that the syllabus for the course as taught that year differs from the current syllabus.)

The course consisted of four parts:-

Part I: Topological Spaces

[DVI], [PDF], [PostScript]

Part II: Covering Maps and the Fundamental Group

[DVI], [PDF], [PostScript]

Part III: Simplicial Homology Theory

[DVI], [PDF], [PostScript]

Part IV: The Topological Classification of Closed Surfaces

[PostScript]

The author, Dr. David Wilkins, <dwilkins@maths.tcd.ie> would very much appreciate being notified of any errors (typographical or others) that you may find in these notes.

Lecture notes for undergraduate courses