TY  - GEN
AU  - Lafontaine,Jacques
TI  - Introduction to differential manifolds
T2  - Grenoble sciences  
SN  - 9783319207346
U1  - 515.36 23
PY  - 2015///
CY  - Cham
PB  - Springer
KW  - Differentiable manifolds.
KW  - Differential Geometry
N1  - Includes bibliographical references and index; 1. Differential Calculus --
2. Manifolds: The Basics --
3. From Local to Global --
4. Lie Groups --
5. Differential Forms --
6. Integration and Applications --
7. Cohomology and Degree Theory --
8. Euler-Poincaré and Gauss-Bonnet --
Appendix --
Bibliography --
Index
N2  - This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. The book should be of interest to various readers: undergraduate and graduate students for a first contact to differential manifolds, mathematicians from other fields and physicists who wish to acquire some feeling about this beautiful theory.
ER  -