$h$-Principles and Flexibility in Geometry (eBook)

Hansjoerg Geiges (Autor)

eBook Download: PDF

58 Seiten
American Mathematical Society (Verlag)
978-1-4704-0377-5 (ISBN)

Infos

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 $C^1$-isometric immersion theory, (iii) 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 (i) and (iii).

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 1-4704-0377-3 / 1470403773
• ISBN-13: 978-1-4704-0377-5 / 9781470403775