Differential Geometry of Singular Spaces and Reduction of Symmetry

Differential Geometry of Singular Spaces and Reduction of Symmetry

by J. Sniatycki

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Overview

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.

Product Details

ISBN-13: 9781107022713
Publisher: Cambridge University Press
Publication date: 06/30/2013
Series: New Mathematical Monographs , #23
Pages: 250
Product dimensions: 6.00(w) x 9.00(h) x 0.70(d)

About the Author

J. niatycki is a professor in the Department of Mathematics at the University of Calgary.

Table of Contents

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; References; Index.

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