Math 2410
time/place: Tu-Th 2:30-3:50 in Kassar 105

instuctor: Prof. Rich Schwartz

my office hours: TBD

course summary
This is a graduate-level course on Algebraic Topology
The main topics are the Fundamental group,
covering spaces, homology, cohomology
and cell complexes.

text: Algebraic Topology by Alan Hatcher
This is a free online book. You can either download
the book or read it online. click here for the book

homework: I will give homework assignments out periodically,
due roughly every 3 weeks.

• HW1 Due Oct 5.
• HW2 Due Nov 2.
• HW3 Due Dec 2.

notes Here are some notes I wrote to supplement the class.

• Van Kampen's Theorem
• Fundamental Groups of 4-Manifolds
• An example continuity proof for homotopies
• Sketch of the Isomorphism Theorem for Universal Covers
• Notes on the fundamental group and first homology
• Excision made easier

grading: I will base the course grades on two things:

• the homework assignments
  
• final exam.
  

syllabus: I plan to cover material from
chapters 0,1,2,3, concentrating on Chapters 1 and 2.
Here is a tentative topic list for the course, in the order I plan to cover them.

• spaces and maps: basic definitions and examples.
• cell complexes
• homotopy, fundamental group basics
• Van Kampen's Theorem
• Covering spaces, deck group, universal cover
• group actions and quotients: lens spaces, hyperbolic manifolds, etc.
• Sperner's Lemma and the Brouwer fixed point theorem
• Singular and simplicial homology basics
• Homotopical invariance of homology
• Excision and exact sequences
• Meyer-Vietoris sequence
• Applications of homology: degrees of maps, fixed point results
• Cohomology basics
• connection between homology and cohomology; universal coefficient theorem.
• connections between cohomology and differential forms.