h-principles and flexibility in geometry / Hansjörg Geiges.

Format:

Book

Author/Creator:

Geiges, Hansjörg, 1966- author.

Series:

Memoirs of the American Mathematical Society ; no. 779.

Memoirs of the American Mathematical Society, 0065-9266 ; number 779

Language:

English

Subjects (All):

Global differential geometry.

Immersions (Mathematics).

Symplectic manifolds.

Physical Description:

1 online resource (74 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2003.

Language Note:

English

Summary:

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.

Contents:

""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Differential Relations and h�Principles""; ""Chapter 3. The h�Principle for open, invariant Relations""; ""3.1. Open, invariant relations""; ""3.2. Statement of the theorem""; ""3.3. Applications""; ""3.4. Proof of the theorem""; ""3.5. Further details of the proof""; ""Chapter 4. Convex Integration Theory""; ""4.1. The h�principle for open, ample relations""; ""4.2. Proof of the simplest case""; ""4.3. Applications to symplectic and contact geometry""; ""Bibliography""

Notes:

"Volume 164, number 779 (first of 5 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0377-3