
Course unit
HOMOLOGY AND COHOMOLOGY
SC02111817, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
MAT/03 
Geometry 
6.0 
Course unit organization
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Prerequisites:

we expect the student knows that it is possible to associate some invariants (fundamental group..), basic commutative algebra. 
Target skills and knowledge:

The student should understand the meaning of invariants for a topological space 
Examination methods:

taylored on the basis of the students attitudes: oral and homeworks. 
Assessment criteria:

some new techniques will be introduced: we expect the student shows how to master them. 
Course unit contents:

Starting from the basic definition of the algebraic topology we will introduce the definition of homology and cohomology for a topological space. Singular, simplicial, cellular, relative, excisin, mayervietoris. Tor and Ext: universal coefficients theorem. Cup and cap product: teh ring structure on the cohomology of a projective space. Poincare' duality 
Planned learning activities and teaching methods:

in class and homeworks 
Additional notes about suggested reading:

we will indicate them during the class: as part of books or/and notes.
J.Rotman "Introduction to algebraic topology" Springer
A. Hatcher "Algebraic Topology" 
Textbooks (and optional supplementary readings) 

Innovative teaching methods: Teaching and learning strategies
 Problem based learning
 Questioning
 Problem solving
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 Latex
Sustainable Development Goals (SDGs)

