MU:MU04070 Algebraic and Diff. Top. III - Course Information
MU04070 Algebraic and Differential Topology III
Mathematical Institute in OpavaWinter 2016
- 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
- Geometry and Global Analysis (programme MU, N1101)
- 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
- Singular homology and cohomology with coefficients; free resolvents, functors Tor and Ext, Universal Coefficient Theorem; Künneth Formula, Eilenberg-Zilber 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.
- Enrolment Statistics (Winter 2016, recent)
- Permalink: https://is.slu.cz/course/sumu/winter2016/MU04070