Scheda programma d'esame
TOPOLOGIA ALGEBRICA
MARIO SALVETTI
Anno accademico2016/17
CdSMATEMATICA
Codice226AA
CFU6
PeriodoSecondo semestre
LinguaItaliano

ModuliSettoreTipoOreDocente/i
TOPOLOGIA ALGEBRICAMAT/03LEZIONI42
FILIPPO GIANLUCA CALLEGARO unimap
MARIO SALVETTI unimap
Programma non disponibile nella lingua selezionata
Learning outcomes
Knowledge
The student who successfully completes the course will be able to demonstrate a solid knowledge of: - methods from Combinatorial Algebraic Topology (as Discrete Morse functions, CW-Morse Theory) - higher homotopy theory (Whithead and Hurewicz theorems, K(pi,1)-spaces) - locally trivial bundles (classifying spaces, obstruction theory, spectral sequences).
Assessment criteria of knowledge
During the oral exam, or seminar presentation, the student must be able to demonstrate his/her knowledge of the course material, having uderstood the main methods and, in case of seminar presentation, being able to understand similar situations where the main tools are used.

Methods:

  • Final oral exam
  • Final essay

Further information:
The evaluation is usually based on a seminar presentation about a subject which is strictly related to the course contents.

Teaching methods

Delivery: face to face

Learning activities:

  • attending lectures
  • participation in seminar

Attendance: Advised

Teaching methods:

  • Lectures
  • Seminar

Syllabus
Discrete Morse Theory, discrete Morse functions, algebraic Morse theory, applications. Higher homotopy groups, CW-approximations, Whithead theorem, Hurewicz theorem, Postnikov towers, Omega spectra and homotopy construction of the cohomology. Fibering and locally trivial bundles, exact sequences of a fibering, principal bundles, classifying spaces and classifyng maps, universal bundles; obstruction theory. Spectral sequences, Leray-Serre spectral sequence; applications.
Bibliography
A Hatcher, "Algebraic Topology", homepage of the author; N, Steenrod, "The Topology of Fibre bundles", Princeton Landmarks in Mathematics; D. Kozlov, "Combinatorial Algebraic Topology", Springer, 2008.
Ultimo aggiornamento 14/11/2016 17:27