ECTS - University of Pisa
Lo studente che completa il corso con successo acquisira' una solida conoscenza dei metodi principali in Topologia Algebrica Combinatoria, conoscenze di base sui gruppi di riflessioni reali, gruppi di Artin e spazi di configurazione, e metodi topologici.
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).
Durante l'esame orale, o la presentazione di un seminario, lo studente deve dimostrare la sua conoscenza del materiale del corso, avendo assimilato i metodi principali e, in caso di presentazione seminariale, di essere in grado di capire situazioni simili a quelle del corso, dove vengono usati gli strumenti principali .
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:
Further information:
The evaluation is usually based on a seminar presentation about a subject which is strictly related to the course contents.
Al termine del corso, lo studente sara' in grado di leggere gran parte degli articoli di ricerca riguardanti la materia; gli studenti che continuino con la ricerca, saranno in generale in grado di applicare i metodi alle problematiche che vengano loro presentate.
By the end of the course, students will be able to understand most of the research papers related to the subject; those who will begin a research career will be able to apply the main tools to the problems which will be presented to them.
Alcuni esercizi verranno lasciati durante il corso, per verificare l'apprendimento delle tecniche fornite. Sara' inoltre possibile prevedere esposizioni di tipo seminariale di argomenti precisi del programma da parte degli auditori.
Some exercises will be given during the course, in order to verify the learning of the proposed techniques. Some seminar talks by students on precise topics will be possible.
Lo studente acquisira' sensibilita' verso una vasta gamma di problematiche all'interno della Matematica attuale e anche nell'ambito di alcune applicazioni della Topologia Algebrica.
Students will acquire an awareness of a wide range of problems in modern Mathematics, as well as of particular applications of Algebraic Topology.
Non vedo significativa differenza tra questa domanda e quella sulla verifica delle capacita'.
I don't see any real difference between this question and the one on "assessment criteria for skills".
Pur non essendo indispensabile, e' molto meglio per lo studente aver seguito con successo il corso di Elementi di Topologia Algebrica previsto dal curriculum.
Even if it is not necessary, it is much better if students had already followed the course Elementi di Topologia Algebrica which is included in the curriculum.
Metodi d'insegnamento:
- lezioni frontali
- seminari
Delivery: face to face
Attendance: Advised
Learning activities:
Teaching methods:
Cofibrations, cofibration sequence;
Fibration and Barratt-Puppe fibration sequence;
Postnikov towers;
K(pi,n) spaces and Whitehead towers;
Representability of cohomology;
Vector bundles and principal bundles;
The classifying space of a group;
Simplicial sets and classifying spaces;
Serre spectral sequence, transgression; Serre classes and applications;
Steenrod squares;
other spectral sequences.
Cofibrations, cofibration sequence;
Fibration and Barratt-Puppe fibration sequence;
Postnikov towers;
K(pi,n) spaces and Whitehead towers;
Representability of cohomology;
Vector bundles and principal bundles;
The classifying space of a group;
Simplicial sets and classifying spaces;
Serre spectral sequence, transgression; Serre classes and applications;
Steenrod squares;
other spectral sequences.
A Hatcher, "Algebraic Topology"
T. tom Dieck, Algebraic Topology, EMS, 2008
E. Spanier, Algebraic Topology, Springer, 1966
Fomenko, Fuchs, Homotopical Topology, GTM 273, Springer, 2016
Steenrod, Topology of fiber bundles, Princeton, 1951
McCleary, A User's guide to spectral sequences, Princeton, 2001
A Hatcher, "Algebraic Topology"
T. tom Dieck, Algebraic Topology, EMS, 2008
E. Spanier, Algebraic Topology, Springer, 1966
Fomenko, Fuchs, Homotopical Topology, GTM 273, Springer, 2016
Steenrod, Topology of fiber bundles, Princeton, 1951
McCleary, A User's guide to spectral sequences, Princeton, 2001
L'esame puo' essere dato con il tradizionale colloquio orale, oppure tramite un seminario su un argomento strettamente connesso agli argomenti e ai metodi svolti.
The exam is made up with one oral test, which can address either a direct verification of topics and tools presented in the course, or a seminar talk regarding some topic which is connected to the material of the course.
