MD133 Differential topology

Faculty of Science
Autumn 2007
Extent and Intensity
2/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. Lukáš Vokřínek, PhD. (lecturer)
Guaranteed by
prof. RNDr. Jan Paseka, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 10:00–11:50 UM
Prerequisites
M5130 Global Analysis && M6140 Topology
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
there are 12 fields of study the course is directly associated with, display
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
Language of instruction
English
Further Comments
The course is taught only once.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2009, Autumn 2013, Spring 2017, Autumn 2022.
  • Enrolment Statistics (Autumn 2007, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2007/MD133