Practical information from SIS. The isis site.
Course evaluation June 3 - June 11. Result of evaluation.
Our textbook will be
The book is available from Universitetsbogladen for DKK 315 (minus student discount) or you may download it directly from the author Allen Hatcher who also maintains a site with updates.
The textbook will be supplemented by the following notes:
The plan is to read Chp 3 - 4 of Hatcher's book. The main topics will be singular, cellular, and simplicial cohomology. The aim is to understand ??.
Your are welcome to suggest topics for the course.
You should know basic general topology: Topological spaces, continuous maps, (locally) connected topological space, (locally) compact topological space, quotient space, manifold. You may use my notes (based on Munkres' book) as a reference. You should also know very basic algebra: Group, ring, vector space, module. You can get an idea of the required prerequisites by leafing through Hatcher's book.
The course is worth 7.5 ECTS. To earn these points you are expected to hand in a number of exercises, to give a number of small presentations in class, and in general to contribute actively to running of the course.
The exercises are: 2.1.14, 3.2.5, 3.2.6. 3.2.7, 3.2.14, 3.3.7,
3.3.10, 4L.2, 4L.5.
See Hatcher's corrections to 3.2.5 og 3.2.14:
Section 3.2, page 229, Exercise 5. Change this to: Show the ring
H^*(RP^{infinity};Z_{2k}) is isomorphic to
Z_{2k}[alpha,beta]/(2alpha,2beta,alpha^2 - k beta) where |alpha|=1 and
|beta|=2. [Use the coefficient map Z_{2k} ---> Z_2 and the proof of
Section 3.2, page 230.
In the next to last line of Exercise 14 the
exponent on alpha should be 2n+1 instead of n+1. (5/28/04)
Theorem 3.12.] (5/28/04)
Bott and Tu: Differential forms in algebraic topology.
Bredon: Geometry and Topology.
Dold: Lectures on Algebraic Topology.
Greenberg and Harper: Algebraic Topology.
Massey: A basic course in algebraic topology.
Jiri Matousek. Using the Borsuk-Ulam Theorem; Lectures on
Topological Methods in Combinatorics and Geometry (Springer
2002).
J.P. May: A concise course in algebraic topology .
Rotman: An introduction to algebraic topology.
Spanier: Algebraic topology.
Switzer: Algebraic topology - homology and homotopy.
Whitehead. Elements of homotopy theory.
George K. Francis: A topological Picture Book.