Course title  Algebraic and Differential Topology I 

Course code  MU/04062 
Organizational form of instruction  Lecture + Lesson 
Level of course  Master 
Year of study  not specified 
Semester  Winter 
Number of ECTS credits  6 
Language of instruction  Czech 
Status of course  Compulsory, Compulsoryoptional 
Form of instruction  Facetoface 
Work placements  This is not an internship 
Recommended optional programme components  None 
Course availability  The course is available to visiting students 
Lecturer(s) 


Course content 
Categories, functors, category Top, Gr a Ab; products and sums, pullback and pushout. 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, simplyconnected spaces. Covering spaces, covering path theorem, covering homotopy theorem, fundamental group, covering mapping theorem Methods of calculation of homotopy groups, Gspaces, fundamental group of the orbit space; SeifertVan Kampen theorem. Superior homotopic groups, exact sequence of the homotopic groups.

Learning activities and teaching methods 
unspecified 
Recommended literature 

Study plans that include the course 
Faculty  Study plan (Version)  Branch of study Category  Recommended year of study  Recommended semester 

Mathematical Institute in Opava  Mathematical Analysis (1IVT)  Mathematics courses  5  Winter 
Mathematical Institute in Opava  Mathematics (1IVT)  Mathematics courses  3  Winter 
Mathematical Institute in Opava  Geometry and Global Analysis (1)  Mathematics courses  1  Winter 
Mathematical Institute in Opava  Mathematics (2F)  Mathematics courses  3  Winter 