Course: Algebraic and Differential Topology II

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Course title Algebraic and Differential Topology II
Course code MU/04063
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Summer
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
Lecturer(s)
  • MARVAN Michal, doc. RNDr. CSc.
  • VOJČÁK Petr, RNDr. Ph.D.
Course content
Chain complexes of Abelian groups, homology, morphisms of chain complexes, algebraic homotopies of chain complex morphisms. Singular simplices, singular chains, singular homology, homotopic invariance of singular homologies. The long exact sequence of homologies, barycentric subdivision, excission, Mayer-Vietors formula. The mapping degree, methods of its calculation. CW-complexes, cellular homologies and their identification with singular homologies.

Learning activities and teaching methods
unspecified
Recommended literature
  • R. M. Switzer. Algebraic Topology - Homotopy and Homology. Berlin.
  • S. Mac Lane. Homology. Springer, Berlin, 1963.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Mathematics (2-F) Mathematics courses 3 Summer
Mathematical Institute in Opava Geometry and Global Analysis (1) Mathematics courses 1 Summer
Mathematical Institute in Opava Mathematics (1-IVT) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 5 Summer