Algebraisk Topologi I E2001 (2 punkter)

Practical information.
The history of topology.

Course Material

We use Allen Hatcher's excellent book on algebraic topology. You can download the book by clicking here.
Background: You can find all the general topology that we'll need in
John Lee: Introduction to Topological Manifolds. Springer GTM 202.
My comments to Chapter 0 (dvi) (pdf
Supplementary reading:
May: A concise course in algebraic topology. Chicago 1999.
Vasiliev: Introduction to Topology.

Exercises

Place your anwers to the exercises in the red folder marked "Algebraisk Topologi I" in the library. You can also find copies of my lecture notes there.

Plan

It is our intention to go through Chp 0 (2 weeks), Chp 1 (6 weeks) and Chp 2 (7 weeks) in Hatcher's book.

What happened last time? What will happen at next lecture?

Date	Lecture	Topics
06.09	Chp 0, pp 1 - 8	(Deformation) retract, homotopy, homotopy equivalence, contractible spaces, CW-complexes, suspension, cone
13.09	Chp 0, pp 9 - 17	Homotopy extension property
20.09	Chp 1, pp 22-30.	The fundamental group, the (unique) homotopy lifting property for covering spaces
27.09	Chp 1, pp 30-45	Functorial properties of the fundamental group. Applications: The fundamental thm of algebra, Brouwer's fixed point thm, Borsuk-Ulam's thm.
04.10	Chp 1, pp 38-44	The van Kampen theorem
11.10	Chp 1, pp 45-50	Applications of van Kampen
18.10	No lecture
25.10	Chp 1, pp.51-58	Covering spaces
01.11	Chp I, pp 59-76	The lifting citerion, the universal covering space
08.11	Chp 1, pp.59-76	Deck transformations, classification of covering spaces.
15.11	Chp 2, pp 106-11	Singular homology. Homotopy invariance.
22.11	Chp 2, pp 111-124	Relative homology. Excision.
29.11	Chp 2, 95-105, 124-132	\Delta-complexes
06.12	Chp 2, 132-144	Cellular homology.
13.12	Chp 2, pp 147-163	Mayer-Vietoris. Coefficients. The formal viewpoint
20.12	Chp 2, 167-174	Applications.

Participants

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