M8131 Algebraic topology 2

Faculty of Science
Spring 2010
Extent and Intensity
2/0. (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. Lukáš Vokřínek, PhD. (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 algebraic topology and algebra.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Advanced course of algebraic topology, the aim is to deeper understanding of homology and homotopy theory.
Syllabus
  • 1. H-spaces and Hopf algebras, loop spaces. 2. Homology and cohomology theories. 3. Spectral sequences. 4. Homology a cohomology of Lie groups and Lie algebras. 5. Vector bundles and characteristic classes.
Literature
  • Hatcher, Allen. Algebraic topology, http://www.math.cornell.edu/~hatcher/AT/ATpage.html
  • 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
Teaching methods
Checked reading.
Assessment methods
Oral exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught only once.
Note related to how often the course is taught: kontrolovaná četba.
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2011 - only for the accreditation.
  • Enrolment Statistics (recent)
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