H-principles and Flexibility in Geometry
2003
American Mathematical Society (Verlag)
978-0-8218-3315-5 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-3315-5 (ISBN)
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The notion of homotopy 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. For a certain differential geometric problem to satisfy the $h$-principle is equivalent to saying that a solution to the problem exists whenever certain topological obstructions vanish.
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.
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.
Introduction Differential relations and $h$-principles The $h$-principle for open, invariant relations Convex integration theory Bibliography.
| Erscheint lt. Verlag | 1.7.2003 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Zusatzinfo | bibliography |
| Verlagsort | Providence |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-8218-3315-4 / 0821833154 |
| ISBN-13 | 978-0-8218-3315-5 / 9780821833155 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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