Modern Geometry— Methods and Applications: Part II: The Geometry and Topology of Manifolds: 104 (Graduate Texts in Mathematics) - Softcover

Dubrovin, B.A.; Fomenko, A.T.; Novikov, S.P.

Softcover

ISBN 10: 1461270111 ISBN 13: 9781461270119

Verlag: Springer, 2012

Inhaltsangabe

Book by Dubrovin BA Fomenko AT Novikov SP

Über diesen Titel

Reseña del editor

Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e.

Reseña del editor

Over the past fifteen years, the geometrical and topological methods of the theory of manifolds have as- sumed a central role in the most advanced areas of pure and applied mathematics as well as theoretical physics. The three volumes of Modern Geometry - Methods and Applications contain a concrete exposition of these methods together with their main applications in mathematics and physics. This third volume, presented in highly accessible languages, concentrates in homology theory. It contains introductions to the contemporary methods for the calculation of homology groups and the classification of manifesto. Both scientists and students of mathematics as well as theoretical physics will find this book to be a valuable reference and text.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2012
• ISBN 10: 1461270111
• ISBN 13: 9781461270119
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 452