An error was encountered while trying to add the item to the cart. Please try again.
Copy To Clipboard
Successfully Copied!
The Moment Maps in Diffeology

Patrick Iglesias-Zemmour CNRS, Marseille, France and Hebrew University of Jerusalem, Israel
Available Formats:
Electronic 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 Click above image for expanded view The Moment Maps in Diffeology Patrick Iglesias-Zemmour CNRS, Marseille, France and Hebrew University of Jerusalem, Israel Available Formats:  Electronic 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.

• 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
• 10. The homogeneous case
• 11. Examples of moment maps in diffeology
• Requests

Review Copy – for reviewers who would like to review an AMS book
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