By Jacques Lafontaine
This ebook is an creation to differential manifolds. It offers strong preliminaries for extra complex subject matters: Riemannian manifolds, differential topology, Lie thought. It presupposes little historical past: the reader is just anticipated to grasp easy differential calculus, and a bit point-set topology. The publication covers the most subject matters of differential geometry: manifolds, tangent house, vector fields, differential kinds, Lie teams, and some extra refined issues equivalent to de Rham cohomology, measure conception and the Gauss-Bonnet theorem for surfaces.
Its ambition is to offer reliable foundations. specifically, the advent of “abstract” notions resembling manifolds or differential kinds is prompted through questions and examples from arithmetic or theoretical physics. greater than one hundred fifty routines, a few of them effortless and classical, a few others extra refined, might help the newbie in addition to the extra professional reader. suggestions are supplied for many of them.
The booklet may be of curiosity to numerous readers: undergraduate and graduate scholars for a primary touch to differential manifolds, mathematicians from different fields and physicists who desire to collect a few feeling approximately this pretty theory.
The unique French textual content advent aux variétés différentielles has been a best-seller in its type in France for plenty of years.
Jacques Lafontaine was once successively assistant Professor at Paris Diderot college and Professor on the collage of Montpellier, the place he's almost immediately emeritus. His major examine pursuits are Riemannian and pseudo-Riemannian geometry, together with a few elements of mathematical relativity. along with his own learn articles, he used to be taken with a number of textbooks and examine monographs.
Read Online or Download An Introduction to Differential Manifolds PDF
Similar geometry & topology books
The 1st of 2 volumes delivering a contemporary creation to Kaehlerian geometry and Hodge constitution. The publication starts off with uncomplicated fabric on advanced variables, complicated manifolds, holomorphic vector bundles, sheaves and cohomology concept, the latter being taken care of in a extra theoretical approach than is common in geometry.
This new (second) variation encompasses a common remedy of quantum box idea (QFT) in an easy scalar box environment as well as the fashionable fabric at the purposes of differential geometry and topology, team concept, and the speculation of linear operators to physics present in the 1st version. a lot of these are brought with out assuming extra heritage at the a part of the reader than a very good beginning in undergraduate (junior) point mathematical physics.
In its easiest shape, Hodge conception is the examine of classes – integrals of algebraic differential kinds which come up within the research of complicated geometry and moduli, quantity thought and physics. prepared round the easy suggestions of adaptations of Hodge constitution and interval maps, this quantity attracts jointly new advancements in deformation conception, reflect symmetry, Galois representations, iterated integrals, algebraic cycles and the Hodge conjecture.
The aim of this ebook, which was once first released in 1978, is to provide an entire account of the idea of permanents, their historical past and functions. This quantity was once the 1st entire account of the speculation of permanents, protecting almost the total of the topic, a characteristic that no uncomplicated survey of the speculation of matrices also can test.
- Algebra and Geometry
- Non-Archimedean Tame Topology and Stably Dominated Types (AM-192) (Annals of Mathematics Studies)
Additional info for An Introduction to Differential Manifolds
An Introduction to Differential Manifolds by Jacques Lafontaine