Course: Algebraic and Differential Topology I

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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, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
  • MARVAN Michal, doc. RNDr. CSc.
  • VOJČÁK Petr, RNDr. Ph.D.
Course content
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.

Learning activities and teaching methods
Recommended literature
  • C. Kosniowski. A First Course in Algebraic Topology. 1980. ISBN 0521298644.
  • S. Mac Lane. Categories for the Working Mathematician. New York, 1971.

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