M8130 Algebraic Topology

Faculty of Science
Autumn 2022
Extent and Intensity
2/2/0. 6 credit(s). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 12:00–13:50 MS1,01016
  • Timetable of Seminar Groups:
M8130/01: Thu 12:00–13:50 M6,01011, M. Čadek
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. Passing the course the students will know basic notions of singular homology and cohomology and homotopy groups and *will be able to use them.
Learning outcomes
- kowledge of basic notions as homology, cohomology and homotopy groups and their properties;
- ability to apply these notions to solve simple problems which are formulated without these notions
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
Teaching methods
Lectures, exercises and homeworks
Assessment methods
Necessary condition for exam is to workout all 10 homeworks during the semester. Exam will be written and oral. Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from tutorials.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught once in two years.
Teacher's information
https://is.muni.cz/auth/ucitel/?fakulta=1431;obdobi=7984
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2002, Spring 2005, Spring 2007, Spring 2009, Spring 2011, spring 2012 - acreditation, Spring 2013, Spring 2015, Spring 2017, Spring 2019, Autumn 2020, Autumn 2024, Spring 2025.
  • Enrolment Statistics (Autumn 2022, recent)
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