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 in a clear and effective way
Prerequisites
General topology.
The course of Geomtria II is necessary for Geometria III
Teaching Methods
Lectures, training sessions, home work
Further information
Office hours: see http://web.math.unifi.it/users/rubei/didattica.html
Type of Assessment
Oral test: questions about theory and exercises to verify the knowledge of theory, the skill to
comunicate the subject ia a clear and effective way, to write mathematics correctely using an appropriate mathematical language
and the skill to apply theory to calculate the main algebraic topology functors
Course program
Fundamental groups, van Kampen theorems, introduction to homological algebra, singular homology, relative homology, homototpy theorem, excision theorem, Mayer-Vietoris theorem, introduction to singular cohomology and duality theorems