(in Polish) Elementy niezmienniczej analizy nieliniowej III
7404-MAT-ENANIII
1. The definition of CW-complexes.
2. Euler characteristic and reduced Euler characteristic (axiomatic definition).
3. Definition of finite G-CW complexes and finite G-CW complexes with a distinguished point.
4. Definition of wedge sum and smash product.
Type of assessment: oral examination
Total student workload
30 hours - lecture
30 hours - studying literature and materials indicated by the lecturers and consultations with the lecturer
30 hours - individual work, exam preparation
Total 90 hours.
3 ECTS points
Learning outcomes - knowledge
After completing the course, the PhD student:
W1: understands the defintion of the CW-complex. (P8S_WG)
W2: understands the concept of cellular decomposition. (P8S_WG)
W3: knows the concept of Euler characteristic and reduced Euler characteristic. (P8S_WG)
W4: knows the properties of the Euler characteristic for finite CW-complexes. (P8S_WG)
W5: understands the definition of a finite G-CW-complex and G-CW-complex with a fixed point. (P8S_WG)
W6: knows the categories of finite G CW-complexes. (P8S_WG)
W7: understands the defintion of wedge sum and smash product of topological spaces with a fixed point. (P8S_WG)
Learning outcomes - skills
After completing the course, the PhD student:
U1: can determine whether a given object is a CW complex. (P8S_UW)
U2: can determine cell distributions for given topological spaces.
(P8S_UW)
U3: can determine the Euler characteristics of finite CW-complexes. (P8S_UW)
U4: can determine whether a given object is a G-CW complex. (P8S_UW)
U5: can determine cell decomposition for given topological spaces with the action of group G. (P8S_UW)
Learning outcomes - social competencies
After completing the course, the PhD student achieves the following results:
K1: understands the appropriate formulation of questions and problems, uses professional terminology correctly (P8S_KK)
K2: analyzes the problem correctly using the principles of logic (P8S_KK)
K3: conveys the acquired knowledge in an understandable way (P8S_KK)
Observation/demonstration teaching methods
- display
Expository teaching methods
- informative (conventional) lecture
Exploratory teaching methods
- practical
- classic problem-solving
Prerequisites
Completed course in mathematical analysis, topology and knowledge of the content of the course Elements of invariant nonlinear analysis I, II. Basic knowledge of algebraic topology will be useful.
Course coordinators
Assessment criteria
Oral exam: W1, W2, W3, W4, W5, W6, W7, U1, U2, U3, U4, U5, K1, K2, K3
Bibliography
1. A. Dold, Lectures on Algebraic Topology, Springer-Verlag Berlin, 1972.
2. T. Dieck, Transformation Groups and Representation Theory, Springer-Verlag, Nowy Jork, 1979.
3. E. H. Spanier, Algebraic topology, McGraw-Hill Book Co, New York-Toronto-London, 1966.
Additional information
Additional information (registration calendar, class conductors,
localization and schedules of classes), might be available in the USOSweb system: