h-Principles and Flexibility in Geometry
- ISBN-10
- 0821833154
- ISBN-13
- 9780821833155
- Category
- Global differential geometry
- Pages
- 58
- Language
- English
- Published
- 2003
- Publisher
- American Mathematical Soc.
- Author
- Hansjörg Geiges
Description
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 Hirsch-Smale immersion theory, Nash-Kuiper $C^1$-isometric immersion theory, existence of symplectic and contact structures on open manifolds. Gromov has developed several powerful methods that allow one to prove $h$-principles. These notes, based on lectures given in the Graduiertenkolleg of Leipzig University, present two such methods which are strong enough to deal with applications Hirsch-Smale immersion theory, and existence of symplectic and contact structures on open manifolds.
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