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.
The course of Geomtria II is necessary for Geometria III
Teaching Methods
Lectures, training sessions, home work
Further information
Office hours: see
the web pages of the teacher and moodle page
Type of Assessment
Written test (about 2 hours, about 6 items) with questions about theory and exercises to verify the knowledge of theory, the skill to write mathematics correctely and the skill to apply theory to calculate the main algebraic topology functors + Oral test to check the knowledge of theory and the skill to apply it in simple exercises, discussion of the written test
Course program
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 and duality theorems