eBook ISBN:  9781470403775 
Product Code:  MEMO/164/779.E 
List Price:  $52.00 
MAA Member Price:  $46.80 
AMS Member Price:  $31.20 
eBook ISBN:  9781470403775 
Product Code:  MEMO/164/779.E 
List Price:  $52.00 
MAA Member Price:  $46.80 
AMS Member Price:  $31.20 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 164; 2003; 58 ppMSC: Primary 53; Secondary 57;
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) HirschSmale immersion theory,
 (ii) NashKuiper \(C^1\)–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).
ReadershipGraduate students and research mathematicians interested in geometry and topology.

Table of Contents

Chapters

1. Introduction

2. Differential relations and $h$principles

3. The $h$principle for open, invariant relations

4. Convex integration theory


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Requests
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) HirschSmale immersion theory,
 (ii) NashKuiper \(C^1\)–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).
Graduate students and research mathematicians interested in geometry and topology.

Chapters

1. Introduction

2. Differential relations and $h$principles

3. The $h$principle for open, invariant relations

4. Convex integration theory