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Fakultät |
Institut für Informatik |
Mathematisches Institut |
MPI für Mathematik in den Naturwissenschaften |
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Universität Leipzig
Fakultät für Mathematik und Informatik
Mathematisches Institut
Graduiertenkolleg - Analysis, Geometrie und ihre Verbindung zu den Naturwissenschaften
Abstract - "h-Principles and Flexibility in Geometry" Hansjörg Geiges (Universiteit Leiden)
The notion of homotopy principle or h-principle is one of the key concepts in an elegant language developed by Gromov to deal with a host of questions in geometry and topology. Roughly speaking, for a certain differential geometric problem to satisfy the h-principle is equivalent to saying that a solution to the problem exists whenever certain obvious topological obstructions vanish.
The foundational examples for applications of Gromov's ideas include
(i) Hirsch-Smale immersion theory,
(ii) Nash-Kuiper C1-isometric immersion theory,
(iii) existence of symplectic and contact structures on open manifolds.
Gromov has developed several powerful methods to prove h-principles. This minicourse presents two such methods which are strong enough to deal with applications (i) and (iii), including convex integration theory. A rough outline of the course is as follows:
- 1st lecture: Introduction to Gromov's language of differential relations and h-principles, applications.
- 2nd and 3rd lecture: The h-principle for open and invariant differential relations.
- 4th and 5th lecture: Convex integration theory, with emphasis on symplectic and contact geometry.
The first lecture is in part meant to be expository. Beyond the introductory part, a basic knowledge of differential topology will be assumed.
Matthias Schwarz
Last modified: Mon Nov 27 10:44:28 MET 2000