3 edition of **Manifolds and Lie Groups** found in the catalog.

Manifolds and Lie Groups

- 73 Want to read
- 35 Currently reading

Published
**January 1, 1981**
by Birkhauser
.

Written in English

- Science/Mathematics,
- Group Theory,
- Mathematics,
- Algebra - General,
- General,
- Mathematics / Group Theory

**Edition Notes**

Contributions | J. Hano (Editor), H. Ozeki (Editor), K. Okamoto (Editor), S. Murakami (Editor), A. Morimoto (Editor) |

The Physical Object | |
---|---|

Format | Hardcover |

Number of Pages | 475 |

ID Numbers | |

Open Library | OL9429640M |

ISBN 10 | 0817630538 |

ISBN 10 | 9780817630539 |

Lie groups are groups (obviously), but they are also smooth manifolds. Therefore, they usually come up in that context. If you want to learn about Lie groups, I recommend Daniel Bump's Lie groups and Anthony Knapp's Lie groups beyond an Introduction. But be aware that you need to know about smooth manifolds before delving into this topic; knowledge of basic group theory . This book treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry.

Manifolds and Lie Groups 64 Differential manifolds 64 Smooth maps and diffeomorphisms 75 Tangent spaces to a manifold 81 Derivatives of smooth maps 90 Immersions and submersions 96 Submanifolds Vector fields Flows and exponential map Frobenius theorem Lie groups and Lie algebras Lie Algebras and Lie Groups Lectures given at Harvard University. Authors Lie Groups. Front Matter. Pages PDF. Complete Fields. Pages Lie Theory. Jean-Pierre Serre. Pages Back Matter. Pages PDF. About this book. Keywords. Lie algebra Lie algebras Lie groups algebra manifolds. Authors and.

Buy Foundations of Differentiable Manifolds and Lie Groups: v. 94 (Graduate Texts in Mathematics) 1st ed. 2nd printing by Warner, Frank W. (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders/5(8). For Galois theory, there is a nice book by Douady and Douady, which looks at it comparing Galois theory with covering space theory etc. Another which has stood the test of time is Ian Stewart's book. For Lie groups and Lie algebras, it can help to see their applications early on, so some of the text books for physicists can be fun to read.

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Manifolds and Lie Groups: Papers In Honor Of Yozô Matsushima (Progress in Mathematics) Softcover reprint of the original 1st ed. Edition by J. Hano (Author) ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book.

Cited by: 5. This book is a good introduction to manifolds and lie groups. Still if you dont have any background,this is not the book to start first chapter is about the basics of manifolds:vector fields,lie brackts,flows on manifolds and more, this chapter can help one alot as a second book on the by: Topological Groups, Lie Groups *immediately available upon purchase as print book shipments may be delayed due to the COVID crisis.

ebook access is temporary and does not include ownership of the ebook. Foundations of Differentiable Manifolds and Lie Groups, Hardcover by Warner, Frank Wilson, ISBNISBNLike New Used, Free shipping in the US Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups/5(13).

The text covers the basics of multilinear algebra, differentiation and integration on manifolds, Lie groups and Lie algebras, homotopy and de Rham cohomology, homology, vector bundles, Riemannian and pseudo-Riemannian geometry, and degree by: 1.

“The book is the first of two volumes on differential geometry and mathematical physics. The present volume deals with manifolds, Lie groups, symplectic geometry, Hamiltonian systems and Hamilton-Jacobi theory.

There are several examples and exercises scattered throughout the book. The presentation of material is well organized and clear. The text covers the basics of multilinear algebra, differentiation and integration on manifolds, Lie groups and Lie algebras, homotopy and de Rham cohomology, homology, vector bundles, Riemannian and pseudo-Riemannian geometry, and degree : Paul Renteln.

Manifolds, Lie Groups, Lie Algebras, with Applications Furthermore, the manifold and the group structure may be nicely compatible and we have a Lie group.

Rn Rn. 4 (see Hilbert and Cohn-Vossen’s classic book). For example, there are the cross-cap, the Steiner roman. sections, I have reorganized the book into twenty-nine sections in seven chapters.

The main additions are Section 20 on the Lie derivative and interior multiplication, two intrinsic operations on a manifold too important to leave out, new criteria in Section 21 for the boundaryorientation, and a new appendixon quaternionsand the symplectic group. Warner, Foundations of Differentiable Manifolds and Lie Groups.

Tu, An Introduction to Manifolds (this is an undergraduate level book, we will assume much of this material). Tu, Differential Geometry: Connections, Curvature and Characteristic Classes. Lee, John, Introduction to. Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups.

It includes differentiable manifolds, tensors and differentiable forms. Lie groups and homogenous spaces, integration on manifolds, and in addition provides a proof of the de Rham theorem via sheaf cohomology.

However, I would argue that one of the best introductions to manifolds is the old soviet book published by MIR, Mishchenko/Fomenko - "A Course of Differential Geometry and Topology". It develops everything up from $\mathbb{R}^n$, curves and surfaces to arrive at smooth manifolds and LOTS of examples (Lie groups, classification of surfaces, etc).

We would like to show you a description here but the site won’t allow more. This book is a good introduction to manifolds and lie groups. Still if you dont have any background,this is not the book to start first chapter is about the basics of manifolds:vector fields,lie brackts,flows on manifolds and more, this chapter can help one alot as a second book on the subject.5/5(3).

Manifolds and Lie Groups Papers in Honor of Yozô Matsushima. Editors (view affiliations) Jun-ichi Hano; On the Orders of the Automorphism Groups of Certain Projective Manifolds.

Alan Howard, Andrew John Sommese. The Tannaka Duality Theorem for Semisimple Lie Groups and the Unitarian Trick. Mitsuo Sugiura. Pages Chapter 1. Lie Groups 1 1. An example of a Lie group 1 2. Smooth manifolds: A review 2 3. Lie groups 8 4. The tangent space of a Lie group - Lie algebras 12 5.

One-parameter subgroups 15 6. The Campbell-Baker-HausdorfT formula 20 7. Lie's theorems 21 Chapter 2. Maximal Tori and the Classification Theorem 23 1. Representation theory: elementary File Size: 8MB. It includes differentiable manifolds, tensors and differentiable forms.

Lie groups and homogenous spaces, integration on manifolds, and in addition provides a proof of the de Rham theorem via sheaf cohomology theory, and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem/5.

Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups.

It includes differentiable manifolds, tensors and differentiable forms. Lie groups and homogenous spaces, integration on manifolds, and in. Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups.

It includes differentiable manifolds, tensors and differentiable forms. Lie groups and homogenous spaces, integration on manifolds, and in addition provides a proof of the de Rham theorem via sheaf cohomology 4/5(2).

Lie groups are smooth differentiable manifolds and as such can be studied using differential calculus, in contrast with the case of more general topological of the key ideas in the theory of Lie groups is to replace the global object, the group, with its local or linearized version, which Lie himself called its "infinitesimal group" and which has since become known as its Lie.

This book is a graduate-level introduction to the tools and structures of modern differential geometry. Included are the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, differential forms, de Rham cohomology, the Frobenius theorem and basic Lie group s: 1.When using this book for a course in Lie Groups, taught by Professor Helgason himself, I found this book severely lacking.

Take for example Chapter I, which covers some basic differential geometry. The definition of a tangent vector is the standard algebraic definition (as derivations of functions on the manifold).Cited by: Differential geometry plays an increasingly important role in modern theoretical physics and applied mathematics.

This textbook gives an introduction to geometrical topics useful in theoretical physics and applied mathematics, covering: manifolds, tensor fields, differential forms, connections, symplectic geometry, actions of Lie groups, bundles, spinors, and so by: