This is a continuation course to Algebraic Topology I. The course will cover more advanced topics in algebraic topology including: homology with coefficients, cohomology of spaces, and Poincaré duality. See also Sara Kalisnik's previous course.
General topology, linear algebra, singular homology of topological spaces (e.g. as taught in Algebraic topology I). Some knowledge of differential geometry and differential topology is useful but not absolutely necessary.
The lectures will take place
All lectures are recorded. The recordings are available here.Office hours are held every week (except during Easter week) on Tuesdays 15:1517:00 by Semyon Abramyan in his office HG FO 27.6. Please let Semyon know by email at what time you are going to come.
Exercise sheets and solutions will be posted here, and will be discussed during office hours.
Sheet 1  Solutions 1 
Sheet 2 (typo in 4a) corrected)  
Sheet 3 
You may pick exercises from the sheets, write up their solutions cleanly in LaTeX, and email them to Lukas Lewark for feedback. After some polishing, your solution will then appear on the metaphor page, so everyone can profit from it. Only one student's solution per exercise: please refer to the following list, and check with Lukas Lewark beforehand that your exercise is really still free.
The handwritten lecture notes will be posted here before every lecture. Here are all lecture notes in a single file. All comments and corrections are highly welcome!
Date  Topics  References  Material 

21 February: Lecture 1 

Tensor products:

Notes, Clicker 
23 February: Lecture 2 

Category Theory:

Notes 
28 February: Lecture 3 

Axioms for homology:

Notes, Clicker 
1 March: Lecture 4 

3. Calculations and the theorem of BorsukUlam:

Notes 
6 March: Lecture 5 

Notes  
8 March: Lecture 6 

4. The Universal Coefficient Theorem for homology:

Notes (version 2) 
13 March: Lecture 7 

Notes, Clicker  
15 March: Lecture 8 

Notes (version 2)  
20 March: Lecture 9 

Cohomology:

Notes 
22 March: Lecture 10 

Notes  
27 March: Lecture 11 

Notes  
29 March – 5 April  Easter  
10 April: Lecture 12 

Cup product:

Notes 
12 April: Lecture 13 

Notes  
17 April: Lecture 14 


19 April: Lecture 15 


24 April: Lecture 16  
26 April: Lecture 17  
1 May  Labour Day  
3 May: Lecture 18  
8 May: Lecture 19  
10 May: Lecture 20  
15 May: Lecture 21  
17 May: Lecture 22  
22 May: Lecture 23  
24 May: Lecture 24  
29 May: Lecture 25  
31 May: Lecture 26 