MD133 Differential topology

Faculty of Science
Autumn 2022
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Taught in person.
Teacher(s)
doc. Lukáš Vokřínek, PhD. (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
Mon 10:00–11:50 MS1,01016
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
This is an introductory course to Differential topology. The topics cover embeddings into euclidean space, tubular neighbourhoods, Sard's theorem, transversality, classification of vector bundles, degree of a map, Pontryagin-Thom construction, index of a vector field, Morse theory and function spaces.
Learning outcomes
Students will be able to understand and work with basic concepts of differential topology, manifolds, submanifolds and vector bundles, their connection to homotopy groups of spheres and compare the various topologies on the function spaces.
Syllabus
  • embeddings into euclidean space, tubular neighbourhoods, Sard's theorem, transversality, classification of vector bundles, degree of a map, Pontryagin-Thom construction, index of a vector field, Morse theory and function spaces
Literature
  • HIRSCH, Morris W. Differential topology. New York [N.Y.]: Springer-Verlag. x, 222. ISBN 3540901485. 1976. info
Teaching methods
standard lectures
Assessment methods
oral examination (for the course completion type examination) or attendance (for the course completion type credit/no-credit)
Language of instruction
English
Further Comments
Study Materials
The course is taught only once.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2007, Autumn 2009, Autumn 2013, Spring 2017.
  • Enrolment Statistics (recent)
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