Math 225C: Algebraic Topology

Date  Tentative topic 
Homework

3/28 (Mon) 
Homotopy and composition of paths 
HW1,
due 4/4 
3/30 (Wed) 
Fundamental groups, Day I 

4/1 (Fri) 
Fundamental groups, Day II (homotopy invariance) 

4/4 
Covering spaces; homotopy lifting property  HW2,
due 4/11 
4/6 
Computation of \pi_1(S^1) and \pi_1(S^n)  
4/8 
Seifertvan Kampen theorem, Day I 

4/11 
Seifertvan Kampen theorem, Day II  HW3,
due 4/18 
4/13 
Computations of \pi_1; universal cover 

4/15 
Universal cover; lifting properties 

4/18 
Classification of covering spaces 
HW4,
due 4/25 
4/20 
Normal covers 

4/22 
\Deltacomplexes  
4/25 
Simplicial homology  HW5,
due 5/2 
4/27 
Singular homology  
4/29 
Functoriality and homotopy invariance  
5/2 
Exact sequences; MayerVietoris
sequence 
HW6,
due 5/9 
5/4 
More on MayerVietoris; Barycentric
subdivision 

5/6 
More on barycentric
subdivision 

5/9 
Relative homology 
HW7,
due 5/16 
5/11 
Excision 

5/13 
Homology and the
fundamental group 

5/16 
Equivalence of simplicial and singular homology;
homology axioms 
HW8,
due 5/23 
5/18 
Degree 

5/20 
Cellular homology  
5/23 
Cellular homology computations  HW9, due 6/3(revised version) 
5/25 
Cohomology, Day I 

5/27 
Cohomology, Day II 

5/30 
University Holiday
(Memorial Day) 

6/1 
Cohomology, Day III 

6/3 
Cup products 

Final exam
is takehome! 