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$h$-Principles and Flexibility in Geometry
 
Hansjörg Geiges University of Cologne, Cologne, Germany
h-Principles and Flexibility in Geometry
eBook ISBN:  978-1-4704-0377-5
Product Code:  MEMO/164/779.E
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $31.20
h-Principles and Flexibility in Geometry
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$h$-Principles and Flexibility in Geometry
Hansjörg Geiges University of Cologne, Cologne, Germany
eBook ISBN:  978-1-4704-0377-5
Product Code:  MEMO/164/779.E
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $31.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1642003; 58 pp
    MSC: 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) 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).

    Readership

    Graduate 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1642003; 58 pp
MSC: 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) 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).

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.