MU04063 Algebraic and Differential Topology II

Mathematical Institute in Opava
Summer 2019
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Marvan, CSc. (lecturer)
doc. RNDr. Michal Marvan, CSc. (seminar tutor)
Guaranteed by
doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava
Prerequisites (in Czech)
MU04062 Algebraic and Diff. Top. I
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
Course objectives
The main theme of the second part of the three-term course in algebraic topologz is singular homology and cohomology.
Syllabus
  • 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.
Literature
    recommended literature
  • R. M. Switzer. Algebraic Topology - Homotopy and Homology. Berlin. info
  • S. Mac Lane. Homology. Springer, Berlin, 1963. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 1997, Summer 1998, Winter 1998, Summer 1999, Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2009, Summer 2010, Summer 2011, Summer 2012, Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2018.
  • Enrolment Statistics (recent)
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