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)
- Keine Verlagsinformationen verfügbar
- Artikel merken
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 |
Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Gekrümmte Kurven und Flächen
Buch | Softcover (2024)
De Gruyter (Verlag)
49,95 €
Buch | Hardcover (2022)
Freies Geistesleben (Verlag)
24,00 €