Universität Wien
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250105 VO Selected topics in Topology (2005W)

Selected topics in Topology

0.00 ECTS (2.00 SWS), SPL 25 - Mathematik

erstmals am 03.10.2005

Details

Language: German

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 03.10. 15:15 - 16:00 Seminarraum
  • Tuesday 04.10. 15:15 - 16:00 Seminarraum
  • Monday 10.10. 15:15 - 16:00 Seminarraum
  • Tuesday 11.10. 15:15 - 16:00 Seminarraum
  • Monday 17.10. 15:15 - 16:00 Seminarraum
  • Tuesday 18.10. 15:15 - 16:00 Seminarraum
  • Monday 24.10. 15:15 - 16:00 Seminarraum
  • Tuesday 25.10. 15:15 - 16:00 Seminarraum
  • Monday 31.10. 15:15 - 16:00 Seminarraum
  • Monday 07.11. 15:15 - 16:00 Seminarraum
  • Tuesday 08.11. 15:15 - 16:00 Seminarraum
  • Monday 14.11. 15:15 - 16:00 Seminarraum
  • Tuesday 15.11. 15:15 - 16:00 Seminarraum
  • Monday 21.11. 15:15 - 16:00 Seminarraum
  • Tuesday 22.11. 15:15 - 16:00 Seminarraum
  • Monday 28.11. 15:15 - 16:00 Seminarraum
  • Tuesday 29.11. 15:15 - 16:00 Seminarraum
  • Monday 05.12. 15:15 - 16:00 Seminarraum
  • Tuesday 06.12. 15:15 - 16:00 Seminarraum
  • Monday 12.12. 15:15 - 16:00 Seminarraum
  • Tuesday 13.12. 15:15 - 16:00 Seminarraum
  • Monday 09.01. 15:15 - 16:00 Seminarraum
  • Tuesday 10.01. 15:15 - 16:00 Seminarraum
  • Monday 16.01. 15:15 - 16:00 Seminarraum
  • Tuesday 17.01. 15:15 - 16:00 Seminarraum
  • Monday 23.01. 15:15 - 16:00 Seminarraum
  • Tuesday 24.01. 15:15 - 16:00 Seminarraum
  • Monday 30.01. 15:15 - 16:00 Seminarraum
  • Tuesday 31.01. 15:15 - 16:00 Seminarraum

Information

Aims, contents and method of the course

Differntial Topology studies global aspects of manifolds.
Manifolds emerge naturally when one is aiming for a coordinate free and
global formulation of analysis.
In many applications manifolds appear as the underlying objects on which
the problems (equations) are formulated; for instance the phase space in
mechanics or the spacetime in relativity.
They become indispensable if one wants to pose and answer global questions.

As central mathematical objects they deserve to be studied thoroughly.
One of the basic questions is: What manifolds are there, and how to tell
them apart?
This question has proven to be very fruitful, leading
to an enormous amount of beautiful mathematics, and still is an active
field of research.

In this lecture course we will discuss fundamental methods used in
differential topology. Among other things, we will prove the (easy) Whitney
embedding theorem, Morse inequalities, and classify compact surfaces
(2-dimensional manifolds.)

Assessment and permitted materials

Minimum requirements and assessment criteria

The aim of the lecture course is to communicate a comprehension of some
fundamental methods and theorems of Differential Topology.

Examination topics

I will assume a good understanding of Analysis 1-3 and
basic concepts from set theoretic Topology. Basic knowledge
of Differential Geometry und Algebraic Topology is helpful
but not necessary.

Reading list

[1] R. Abraham and J. Robbin
Transversal Mappings and Flows.
W.A. Benjamin, Inc., New York-Amsterdam 1967.

[2] M.W. Hirsch,
Differential Topology.
Corrected reprint of the 1976 original.
Graduate Texts in Mathematics 33.
Springer-Verlag, New York, 1994.

[3] T. Broecker und K. Jaenich,
Einfuehrung in die Differentialtopologie.
Heidelberger Taschenbuecher, Band 143.
Springer-Verlag, Berlin-New York, 1973.

[4] J. Milnor,
Morse Theory.
Annals of Mathematics Studies 51.
Princeton University Press, Princeton, N.J. 1963.

[5] Y. Matsumoto,
An Introduction to Morse Theory.
Translations of Mathematical Monographs 208.
Iwanami Series in Modern Mathematics.
American Mathematical Society, Providence, RI, 2002.

Association in the course directory

Last modified: Mo 07.09.2020 15:40