h-principles and flexibility in geometry
Author(s)
Bibliographic Information
h-principles and flexibility in geometry
（Memoirs of the American Mathematical Society, no. 779）
American Mathematical Society, 2003
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Note
Includes bibliographical references (p. 57-58)
"July 2003, volume 164, number 779 (first of 5 numbers)"
Description and Table of Contents
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.
Table of Contents
Introduction Differential relations and $h$-principles The $h$-principle for open, invariant relations Convex integration theory Bibliography.
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