By Peter W. Michor

ISBN-10: 0821820036

ISBN-13: 9780821820032

ISBN-10: 0821843443

ISBN-13: 9780821843444

ISBN-10: 1719553904

ISBN-13: 9781719553902

ISBN-10: 1819563383

ISBN-13: 9781819563382

ISBN-10: 2419837657

ISBN-13: 9782419837651

ISBN-10: 3619893233

ISBN-13: 9783619893232

ISBN-10: 3919822692

ISBN-13: 9783919822697

ISBN-10: 4819984454

ISBN-13: 9784819984454

ISBN-10: 6519573914

ISBN-13: 9786519573914

This booklet treats the basics of differential geometry: manifolds, flows, Lie teams and their activities, invariant thought, differential kinds and de Rham cohomology, bundles and connections, Riemann manifolds, isometric activities, and symplectic and Poisson geometry. The structure of the fabric stresses naturality and functoriality from the start and is as coordinate-free as attainable. Coordinate formulation are constantly derived as additional details. a few appealing strange features of this ebook are as follows: preliminary submanifolds and the Frobenius theorem for distributions of nonconstant rank (the Stefan-Sussman idea) are mentioned. Lie teams and their activities are taken care of early on, together with the slice theorem and invariant thought. De Rham cohomology comprises that of compact Lie teams, resulting in the learn of (nonabelian) extensions of Lie algebras and Lie teams. The Frolicher-Nijenhuis bracket for tangent package deal valued differential types is used to specific any type of curvature and moment Bianchi identification, even for fiber bundles (without constitution groups). Riemann geometry starts off with a cautious remedy of connections to geodesic buildings to sprays to connectors and again to connections, going through the second one and 3rd tangent bundles. The Jacobi circulate at the moment tangent package is a brand new point coming from this perspective. Symplectic and Poisson geometry emphasizes team activities, momentum mappings, and mark downs. This e-book supplies the cautious reader operating wisdom in a variety of subject matters of contemporary coordinate-free differential geometry in now not too many pages. A prerequisite for utilizing this ebook is an efficient wisdom of undergraduate research and linear algebra.