PřF:M8130 Algebraic Topology - Course Information

M8130 Algebraic Topology

Faculty of Science
Spring 2007

Extent and Intensity

4/0/0. 4 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).

Teacher(s)

doc. RNDr. Martin Čadek, CSc. (lecturer)

Guaranteed by

Timetable

Tue 14:00–15:50 UM, Thu 14:00–15:50 UM

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. Zkouška bude písemka a ústní zkouška.

Language of instruction

Czech

Further Comments

The course is taught once in two years.

Teacher's information

http://www.math.muni.cz/~cadek