M8130 Algebraic Topology

Faculty of Science
Spring 2015
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). 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
Tue 8:00–9:50 M6,01011
  • Timetable of Seminar Groups:
M8130/01: Wed 8:00–9:50 M6,01011
Prerequisites
Basic notions from general topology and algebra.
Course Enrolment Limitations
The course is offered to students of any study field.
Abstract
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.
Key topics
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
Study resources and 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
Approaches, practices, and methods used in teaching
Lectures, exercises and homeworks
Method of verifying learning outcomes and course completion requirements
Exam written and oral. Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from exercises
Language of instruction
Czech
Further Comments
Study Materials
The course is taught once in two years.
Teacher's information
http://www.math.muni.cz/~cadek
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 2017, Spring 2019, Autumn 2020, Autumn 2022, Autumn 2024, Autumn 2026.
  • Enrolment Statistics (Spring 2015, recent)
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