M7880 Algebraic topology

Faculty of Science
Autumn 2000
Extent and Intensity
4/0/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Čadek, CSc.
Prerequisites
Basic notions from general topology and algebra.
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
Basic course of algebraic topology, introduction to singular homology and cohomology and homotopy groups.
Syllabus
  • 1. Motivation 2. Basic constructions 3. CW complexes 4. Singular homology and cohomology 5. Homological algebra 6. Products and Kuennet formula 7. Thom isomorphism and Gyzin sequence 8. Poincaré duality 9. Homotopy groups 10.Cofibrations and fibrations 11.Whitehead theorem 12.Hurewicz theorem
Literature
  • Hatcher, Allen. Algebraic topology I. http://math.cornell.edu/~hatcher
  • BREDON, Glen E. Topology and geometry. New York: Springer-Verlag, 1993, 557 s. ISBN 0-387-97926-3. info
  • Spanier, Edwin H. Algebraic topology. New York: McGraw-Hill Book Company, 1966
  • DOLD, Albrecht. Lekcii po algebraičeskoj topologii. Moskva: Mir, 1976, 463 s. info
  • Switzer, Robert M. Algebraic topology - homology and homotopy. New York: Springer-Verlag, 1975.
  • WHITEHEAD, George W. Elements of homotopy theory. New York: Springer-Verlag, 1978, xxi, 744 s. ISBN 0-387-90336-4-. info
Assessment methods (in Czech)
Přednáška dvakrát týdně po dvou hodinách. Na přednáškách budou zadávány průběžné domácí úkoly. Jejich hodnocení bude tvořit 30% zkoušky. Další část zkoušky bude písemka a ústní zkouška.
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught only once.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~cadek
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