Mihai-Dinu Lazarescu: Lens spaces

Abstract: Lens spaces are identication spaces. Their denition involves two parameters p
and q. As a rst easier example of an identication space I will construct the Mobius strip.
Then I will give three dierent recipes for constructing lens spaces. Furthermore, I classify them into homeomorphic classes.
Next I dene homotopies, homotopy equivalence and the fundamental group. The fundamental group lives esentially in two-dimensional space. For higher dimensions we will use homology groups. The parameter p is essential for homology.
Ideally, if time permits, I should like to show that lens spaces which are not homeomorphic
can very well be homotopically equivalent. This depends strongly on the parameter q.
Handledare: Rikard Bogvad