Homotopy Theory
4 hours of lectures per week.
Lecturer
Jørgen Tornehave
Content
The general theme in the course will be to study the set $[X,Y]$ of based homotopy classes of maps between spaces $X,Y$ with basepoint. When $X$ is the $n$-sphere we get the $n$'th homotopy group $\pi_n(Y)$, Dually $Y$ might be an Eilenberg MacLane space $K(\pi,n)$, and then $[X,Y]$ is in 1-1 correspondence with the singnlar cohomology groups $H^n(X,\pi)$. This along with the Serre spectral requence makes the method of killing homotopy groups work. We shall see how this machinery leads to Serre's finiteness theorem: The group $\pi_n(S^k)$ are finite with a few known exceptions.
Prerequisites
The course
Homotopy and Homology E2003.
Literature
Allen Hatcher,
Algebraic Topology, Cambridge University Press, 2002 plus supplementary material.
Evaluation
Students who do not intend to take a degree in Mathematics or Statistics from the University of Aarhus, but wish to earn credits for a 2.dels course from the Department of Mathematics, should indicate at the beginning of the course that they wish to be examined.
The form of examination for these students will be active participation together with oral or written contributions.
Credits
10 ECTS
Quarter
Spring 2004