1.

Record Nr.

UNINA9910452484303321

Autore

Śniatycki Jędrzej

Titolo

Differential geometry of singular spaces and reduction of symmetry / / J. Śniatycki, Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada [[electronic resource]]

Pubbl/distr/stampa

Cambridge : , : Cambridge University Press, , 2013

ISBN

1-139-88895-1

1-107-05451-6

1-107-05905-4

1-139-13699-2

1-107-05559-8

1-107-05780-9

1-107-05668-3

Descrizione fisica

1 online resource (xii, 235 pages) : digital, PDF file(s)

Collana

New mathematical monographs ; ; 23

Disciplina

516.3/6

Soggetti

Geometry, Differential

Function spaces

Symmetry (Mathematics)

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Preface -- 1. Introduction -- Part I. Differential Geometry of Singular Spaces: 2. Differential structures; 3. Derivations; 4. Stratified spaces; 5. Differential forms -- Part II. Reduction of Symmetries: 6. Symplectic reduction; 7. Commutation of quantization and reduction; 8. Further examples of reduction.

Sommario/riassunto

In this book the author illustrates the power of the theory of subcartesian differential spaces for investigating spaces with singularities. Part I gives a detailed and comprehensive presentation of the theory of differential spaces, including integration of distributions on subcartesian spaces and the structure of stratified spaces. Part II presents an effective approach to the reduction of symmetries. Concrete applications covered in the text include reduction of symmetries of Hamiltonian systems, non-holonomically constrained



systems, Dirac structures, and the commutation of quantization with reduction for a proper action of the symmetry group. With each application the author provides an introduction to the field in which relevant problems occur. This book will appeal to researchers and graduate students in mathematics and engineering.