Memoirs of the American Mathematical Society 2010; 72 pp; softcover Volume: 207 ISBN10: 0821847090 ISBN13: 9780821847091 List Price: US$68 Individual Members: US$40.80 Institutional Members: US$54.40 Order Code: MEMO/207/972
 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 2form \(\omega\), 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 leftinvariant 1forms 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  Introduction
 Few words about diffeology
 Diffeological groups and momenta
 The paths moment map
 The 2points moment map
 The moment maps
 The moment maps for exact 2forms
 Functoriality of the moment maps
 The universal moment maps
 About symplectic manifolds
 The homogeneous case
 Examples of moment maps in diffeology
 Bibliography
