The moment maps in diffeology / Patrick Iglesias-Zemmour.

Format:

Book

Author/Creator:

Iglesias-Zemmour, Patrick, 1953-

Series:

Memoirs of the American Mathematical Society ; no. 972.

Memoirs of the American Mathematical Society, 0065-9268 ; no. 972

Language:

English

Subjects (All):

Symplectic geometry.

Physical Description:

v, 72 pages : illustrations ; 26 cm.

Place of Publication:

Providence, R.I. : American Mathematical Society, 2010.

Summary:

"This memoir presents a generalization of the moment maps to the category {Diffeology}. This construction applies to every smooth action of any diffeological group G preserving a closed 2-form w, defined on some diffeological space X. In particular, that reveals a universal construction, associated to the action of the whole group of automorphisms Diff (X, w). By considering directly the space of momenta of any diffeological group G, that is the space g* of left-invariant 1-forms on 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."--Publisher's description.

Contents:

Few words about diffeology

Diffeological groups and momenta

The paths moment map

The 2-points moment map

The moment maps

The moment maps for exact 2-forms

Functoriality of the moment maps

The universal moment maps

About symplectic manifolds

The homogeneous case

Examples of moment maps in diffeology.

Notes:

"Volume 207, number 972 (second of 5 numbers)."

Includes bibliographical references (pages 71-72).

ISBN:

9780821847091

0821847090

OCLC:

643081618