MD133 Differential topology

Faculty of Science
Autumn 2026
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).
In-person direct teaching
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
Course Enrolment Limitations
The course is offered to students of any study field.
Abstract
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.
Key topics
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
Study resources and literature
  • HIRSCH, Morris W. Differential topology. New York [N.Y.]: Springer-Verlag, 1976, x, 222. ISBN 3540901485. info
Approaches, practices, and methods used in teaching
standard lectures
Method of verifying learning outcomes and course completion requirements
oral examination (for the course completion type examination) or attendance (for the course completion type credit/no-credit)
Language of instruction
English
Further Comments
The course is taught only once.
The course is taught every week.
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, Autumn 2022.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2026/MD133