Homotopy theory, fall 2015

The [toc] macro is a standalone macro and it cannot be used inline. Click on this message for details.
This macro generates standalone content. As a consequence you need to make sure to use a syntax that separates your macro from the content before and after it so that it's on a line by itself. For example in XWiki Syntax 2.0+ this means having 2 newline characters (a.k.a line breaks) separating your macro from the content before and after it.

News

•  The course starts on Wednesday, 2nd of September (no lecture on Monday 31st of August). On Thursday, 3rd of September, there will be an extra lecture (12-14, B321).

Teaching schedule

Weeks 36-42 and 44-50, Monday 10-12 and Wednesday 14-16 in room C124. In addition, two hours of exercise classes per week. Guidance in Ratkomo (3rd floor corridor) on Wednesdays 10-12.

Exams

One exam at the end of the course, on Monday 21st of December, 10-14, auditorium A111.

Course material

Lecture notes (in Finnish):htteoria.pdf

Liite:Parakompaktisuus.pdf

Metsänkylä-Näätänen: Algebra, p. 92-98:D4.pdf

In English: W. S. Massey: Algebraic topology: an introduction; A. Hatcher: Algebraic topology; E. H. Spanier: Algebraic topology

Preliminary schedule:

1. Homotopy of mappings; path homotopy; fundamental group; covering map; the fundamental group of a circle; examples.
2. Applications: Brouwer's fixed point theorem and Borsuk-Ulam theorem (in dimension 2); fundamental theorem of algebra.
3. More about covering spaces; monodromy theorems; connection with the fundamental group; classification of covering maps; universal covering space.
4. Higher homotopy groups; examples of homotopy groups of spheres; the Hopf mapping S^3 -> S^2; Freudenthal suspension.
5. Relative homotopy groups; exact homotopy sequences.

Registration

 
Did you forget to register? What to do?

Exercises

Assignments

• Exercise 1 (10.9.2015): h1t.pdf,h1r.pdf
• Exercise 2 (17.9.2015): h2t.pdf,h2r.pdf
• Exercise 3 (24.9.2015): h3t.pdf,h3r.pdf
• Exercise 4 (1.10.2015): h4t.pdf,h4r.pdf
• Exercise 5 (8.10.2015): h5t.pdf,h5r.pdf
• Exercise 6 (15.10.2015): h6t.pdf,h6r.pdf
• Exercise 7 (29.10.2015): h7t.pdf,h7r.pdf
• Exercise 8 (5.11.2015): h8t.pdf,h8r.pdf
• Exercise 9 (12.11.2015): h9t.pdf,h9r.pdf
• Exercise 10 (19.11.2015): h10t.pdf,h10r.pdf
• Exercise 11 (26.11.2015): h11t.pdf,h11r.pdf
• Exercise 12 (3.12.2015): h12t.pdf,h12r.pdf
• Exercise 13 (10.12.2015): h13t.pdf,h13r.pdf

Exercise classes

Course feedback

Course feedback can be given at any point during the course. Click here.