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ALGEBRAIC TOPOLOGY
MARIO SALVETTI
Academic year2016/17
CourseMATHEMATICS
Code226AA
Credits6
PeriodSemester 2
LanguageItalian
CourseMATHEMATICS
Code226AA
Credits6
PeriodSemester 2
LanguageItalian
Syllabus not available in selected language
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.
Updated: 14/11/2016 17:27