Second Level Degree in Mathematics
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HOMOLOGY AND COHOMOLOGY - 6 CFU
Teacher
Bruno Chiarellotto
Scheduled Period
I Year - 2 Semester | 28/02/2022 - 11/06/2022
Hours: 48 (48 lezione)
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: written and homeworks during the semester.
Assessment criteria
some new techniques will be introduced: we expect the student shows how to master them.
Course 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, mayer-vietoris. Tor and Ext: universal coefficients theorem. Cup and cap product: teh ring structure on the cohomology of a projective space and some other particular topological spaces. Eventually 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"