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Topics In The Differential Geometry of Supermanifolds: Super Holonomy Theorem - Couverture souple

Ayine, Gabriel

 
9783639043075: Topics In The Differential Geometry of Supermanifolds: Super Holonomy Theorem
Couverture souple
ISBN 10 : 3639043073 ISBN 13 : 9783639043075
Editeur : VDM Verlag Dr. Müller, 2008

Synopsis

The book combines the algebraic and differential geometric approaches to supermanifold theory. It begins with a superspace, constructed by taking the Cartesian product of copies of the even and odd parts of an infinite-dimensional Banach Grassmann algebra. The superspace serves as a model space of G-infinite supermanifolds. The theory of super Lie groups and super Lie algebras, (in particular the existence theorems on super Lie groups) is given. Super principal fiber bundles equipped with connections and the action of super Lie groups and supervector fields are introduced. The concept of parallel transport along smooth curves is introduced in the same way as in conventional differential geometry. It is shown that a smooth curve in the base space can be lifted uniquely into the bundle and that parallel displacements along closed smooth curves form a group, the ¿super holonomy group¿. It is further shown that the group is a sub-super Lie group of the structure group of the bundle. The result follows from the super analogues of the Freudenthal theorem and the reduction theorem of bundles. The book concludes with a proof of a super version of the Ambrose-Singer holonomy theorem.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

The book combines the algebraic and differential geometric approaches to supermanifold theory. It begins with a superspace, constructed by taking the Cartesian product of copies of the even and odd parts of an infinite-dimensional Banach Grassmann algebra. The superspace serves as a model space of G-infinite supermanifolds. The theory of super Lie groups and super Lie algebras, (in particular the existence theorems on super Lie groups) is given. Super principal fiber bundles equipped with connections and the action of super Lie groups and supervector fields are introduced. The concept of parallel transport along smooth curves is introduced in the same way as in conventional differential geometry. It is shown that a smooth curve in the base space can be lifted uniquely into the bundle and that parallel displacements along closed smooth curves form a group, the ¿super holonomy group¿. It is further shown that the group is a sub-super Lie group of the structure group of the bundle. The result follows from the super analogues of the Freudenthal theorem and the reduction theorem of bundles. The book concludes with a proof of a super version of the Ambrose-Singer holonomy theorem.

Biographie de l'auteur

Education: Univ. of Cape Coast, 1977- 81; BS Math, Dip. Ed. University of Ghana 1989-91; MPhil Math Physics. Howard Univ 1992-2002; Ph.D. GWU 2006 -08; Grad Cert. Survey Design. Employment: Assoc. Professor of Math Howard Community College 1995-present. Honoree in ¿Who¿s Who Among America¿s Teachers¿ in 2003-04, 2004-05, and 2005-06.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
VDM Verlag Dr. Müller
Date d'édition
2008
Langue
anglais
ISBN 10 
3639043073
ISBN 13 
9783639043075
Reliure
Broché
Nombre de pages
88
Coordonnées du fabricant
non disponible
Personne responsable
non disponible