M. J. Greenberg and J. Harper, Algebraic topology a first course, Perseus Books, 1981.
A. Hatcher, Algebraic topology, Cambridge University Press, 2002
Learning Objectives
Knowledge and comprehension of the theory of fundamental groups and of singular homology; skill to apply theory to calculate autonomously the main functors of algebraic topology; skill to present theory both in oral form and in written form
Prerequisites
General topology
Teaching Methods
Lectures, training sessions, home work
Type of Assessment
Written test (about 2 hours, about 6 items) with quetions about theory and exercises + Oral test to check the knowledge of theory and the skill to apply it in simple exercises, discussion of the written test
Course program
Coverings, compact surfaces, fundamental groups, van Kampen theorems, introduction to homological algebra, singular homology, relative homology, homototpy theorem, excision theorem, Mayer-Vietoris theorem, introduction to singular cohomology