Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
The Moment Maps in Diffeology
 
Patrick Iglesias-Zemmour CNRS, Marseille, France and Hebrew University of Jerusalem, Israel
The Moment Maps in Diffeology
eBook ISBN:  978-1-4704-0586-1
Product Code:  MEMO/207/972.E
List Price: $68.00
MAA Member Price: $61.20
AMS Member Price: $40.80
The Moment Maps in Diffeology
Click above image for expanded view
The Moment Maps in Diffeology
Patrick Iglesias-Zemmour CNRS, Marseille, France and Hebrew University of Jerusalem, Israel
eBook ISBN:  978-1-4704-0586-1
Product Code:  MEMO/207/972.E
List Price: $68.00
MAA Member Price: $61.20
AMS Member Price: $40.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2072010; 72 pp
    MSC: Primary 53;

    This memoir presents a generalization of the moment maps to the category \(\{\)Diffeology\(\}\). This construction applies to every smooth action of any diffeological group \(\mathrm{G}\) preserving a closed 2-form \(\omega\), defined on some diffeological space \(\mathrm{X}\). In particular, that reveals a universal construction, associated to the action of the whole group of automorphisms \(\mathrm{Diff}(\mathrm{X},\omega)\). By considering directly the space of momenta of any diffeological group \(\mathrm{G}\), that is the space \(\mathscr{G}^*\) of left-invariant 1-forms on \(\mathrm{G}\), this construction avoids any reference to Lie algebra or any notion of vector fields, or does not involve any functional analysis. These constructions of the various moment maps are illustrated by many examples, some of them originals and others suggested by the mathematical literature.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. Few words about diffeology
    • 2. Diffeological groups and momenta
    • 3. The paths moment map
    • 4. The 2-points moment map
    • 5. The moment maps
    • 6. The moment maps for exact 2-forms
    • 7. Functoriality of the moment maps
    • 8. The universal moment maps
    • 9. About symplectic manifolds
    • 10. The homogeneous case
    • 11. Examples of moment maps in diffeology
  • 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: 2072010; 72 pp
MSC: Primary 53;

This memoir presents a generalization of the moment maps to the category \(\{\)Diffeology\(\}\). This construction applies to every smooth action of any diffeological group \(\mathrm{G}\) preserving a closed 2-form \(\omega\), defined on some diffeological space \(\mathrm{X}\). In particular, that reveals a universal construction, associated to the action of the whole group of automorphisms \(\mathrm{Diff}(\mathrm{X},\omega)\). By considering directly the space of momenta of any diffeological group \(\mathrm{G}\), that is the space \(\mathscr{G}^*\) of left-invariant 1-forms on \(\mathrm{G}\), this construction avoids any reference to Lie algebra or any notion of vector fields, or does not involve any functional analysis. These constructions of the various moment maps are illustrated by many examples, some of them originals and others suggested by the mathematical literature.

  • Chapters
  • Introduction
  • 1. Few words about diffeology
  • 2. Diffeological groups and momenta
  • 3. The paths moment map
  • 4. The 2-points moment map
  • 5. The moment maps
  • 6. The moment maps for exact 2-forms
  • 7. Functoriality of the moment maps
  • 8. The universal moment maps
  • 9. About symplectic manifolds
  • 10. The homogeneous case
  • 11. Examples of moment maps in diffeology
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.