MU:MU04062 Algebraic and Diff. Top. I - Course Information
MU04062 Algebraic and Differential Topology I
Mathematical Institute in OpavaWinter 2011
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- Guaranteed by
- doc. RNDr. Tomáš Kopf, Ph.D.
Mathematical Institute in Opava - Prerequisites
- Tady jsou uvedené předpoklady ENG
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Geometry (programme MU, M1101)
- Geometry (programme MU, N1101)
- Mathematical Analysis (programme MU, M1101)
- Mathematics (programme MU, B1101)
- Course objectives
- Algebraic topology studies topological spaces by algebraic means. Among its typical problems is the issue of finding out whether on topological space can be continuously mapped onto another. A positive answer may be obtained by constructing such a map but a negative answer may be more difficult to get. In this four-term course on algebraic topology, algebraic methods to solve such problems will be consecutively acquired. This first term, the foundations of homotopy are taught. Homotopies will be met during all four terms of the course. Minimal preliminary knowledge on topology and algebraic structures will be sufficient.
- Syllabus
- Categories, functors, category Top, Gr a Ab; products and sums, pull-back and push-out.
Homotopy of continuous mappings, relative homotopy; homotopical equivalence of topological spaces, contractibility.
Category Top_h, functors in algebraic topology, elementary problems of algebraic topology, homotopy extension property, Borsuk pairs.
Paths and loops, fundamental group, simply-connected spaces.
Covering spaces, covering path theorem, covering homotopy theorem, fundamental group, covering mapping theorem
Methods of calculation of homotopy groups, G-spaces, fundamental group of the orbit space; Seifert-Van Kampen theorem.
Superior homotopic groups, exact sequence of the homotopic groups.
- Categories, functors, category Top, Gr a Ab; products and sums, pull-back and push-out.
- Literature
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
- Teacher's information
- Tady jsou uvedeny požadavky na studenta ENG.
- Enrolment Statistics (Winter 2011, recent)
- Permalink: https://is.slu.cz/course/sumu/winter2011/MU04062