MU04070 Algebraic and Differential Topology III

Mathematical Institute in Opava
Winter 2018
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Guaranteed by
doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava
Prerequisites (in Czech)
MU04063 Algebraic and Diff. Top. II && MU03039 Differential Geometry II
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 third part of this four-term course introduces singular homologies and cohomologies with arbitrary coefficients and basic cohomological operations. In the case of smooth manifolds, the equality of cohomology with coefficients in R and of de Rham cohomology.
Syllabus
  • Singular homology and cohomology with coefficients; free resolvents, functors Tor and Ext, Universal Coefficient Theorem; Künneth Formula, Eilenberg-Zilber Theorem.
    Cohomological operations.
    Basic sheaf theory, acyclic resolvents, abstract and special de Rham theorem
Literature
    recommended literature
  • R. M. Switzer. Algebraic Topology - Homotopy and Homology. Berlin. 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 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2019.
  • Enrolment Statistics (Winter 2018, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2018/MU04070