A global formulation of the Lie theory of transportation groups / Richard S. Palais.

Format:

Book

Author/Creator:

Palais, Richard S., author.

Series:

Memoirs of the American Mathematical Society ; 22.

Memoirs of the American Mathematical Society ; number 22

Language:

English

Subjects (All):

Lie groups.

Transformations (Mathematics).

Physical Description:

1 online resource (130 pages)

Place of Publication:

Providence, R.I. : American Mathematical Society, [1957]

Language Note:

English

Contents:

""Contents""; ""Preface""; ""Acknowledgments""; ""Chapter I: QUOTIENT MANIFOLDS DEFINED BY FOLIATIONS""; ""1. Differentiable Manifolds""; ""2. Foliations""; ""3. The Continuation Theorem""; ""4. Regularity""; ""5. Quotient Manifolds""; ""6. Factorization of Mappings""; ""7. Projection-like Mappings""; ""8. The Uniqueness Theorem""; ""9. Products of Quotient Manifolds""; ""Chapter II: LOCAL AND INFINITESIMAL TRANSFORMATION GROUPS""; ""1. Notation""; ""2. Elementary Definitions""; ""3. 'Factoring' a Transformation Group""; ""4. The Infinitesimal Graph""; ""5. The Local Existence Theorem""

""6. The Uniqueness Theorem""""7. The Existence Theorem""; ""Chapter III: GLOBALIZABLE INFINITESIMAL TRANSFORMATION GROUPS""; ""1. Globalizations""; ""2. Univalent Infinitesimal Transformation Groups""; ""3. Maximum Local Transformation Groups""; ""4. The Principal Theorem""; ""5. Proper Infinitesimal Transformation Groups""; ""6. Uniform Infinitesimal Transformation Groups""; ""7. R-Transformation Groups""; ""8. The Need for Non-Hausdorff Manifolds""; ""9. Can Theorem XX Be Generalized?""; ""Chapter IV: LIE TRANSFORMATION GROUPS""; ""1. Two Theorems on Lie Groups""

""2. Infinitesimal Groups"" ""3. Connected Lie Transformation Groups""; ""4. Lie Transformation Groups""; ""5. Tensor Structures and Their Automorphism Groups""; ""Appendix to Chapter IV""; ""1. Compact-Open Topology""; ""2. Making a Topology Locally Arcwise Connected""; ""3. The Modified Compact-Open Topology""; ""4. Weakening the Topology of a Lie Group""; ""Terminological Index""; ""References""; ""Fixed Notations""

Notes:

Cover title.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-8218-9964-3