Laurea Magistrale in Matematica
Salta il menu di secondo livelloHOMOLOGY AND COHOMOLOGY - 6 CFU
Insegnante
Bruno Chiarellotto
Periodo
I Anno - 2 Semestre | 28/02/2022 - 11/06/2022
Ore: 48 (48 lezione)
Prerequisiti
Ci si aspetta che lo studente abbia gia' visto la possibilita' di associare degli invarianti a spazi topologici (gruppo fondamentale..). Basic commutative algebra.
Conoscenze e abilità da acquisire
The student should understand the meaning of invariants for a topological space
Modalità di esame
taylored on the basis of the students attitudes: written and homeworks during the semester.
Criteri di valutazione
some new techniques will be introduced: we expect the student shows how to master them.
contenuti
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.
Attività di apprendimento previste e metodologie di insegnamento
in class and homeworks.
Eventuali indicazioni sui materiali di studio
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"