MD133 Differential topology

Faculty of Science
Autumn 2009
Extent and Intensity
2/0. 2 credit(s) (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
M5130 Global Analysis && M6140 Topology
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The basic notions of differential topology are explained: transversality, degree of a map and the connection to Euler characteristics, Pontryagin-Thom construction and the cobordism ring, Whitney's embedding theorem.
Syllabus
  • 1. Sard's theorem 2. Transversality 3. The mod 2 degree of a smooth map 4. Degree of a map between oriented manifolds 5. Pontryagin-Thom construction 6. Thom's theorem 7. Whitney's immersion and embedding theorem 8. Two topologies on the set of smooth maps
Literature
  • Milnor, J. W. - Topology from the Differentiable Viewpoint
  • Hirsch, M. W. - Differential Topology
Assessment methods
There are no lectures, students read Hirsch's book Differential Topology.
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 2013, Spring 2017, Autumn 2022.
  • Enrolment Statistics (Autumn 2009, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2009/MD133