Read e-book online A Short Course in Differential Geometry and Topology PDF

By A. T. Fomenko

ISBN-10: 1904868320

ISBN-13: 9781904868323

Read or Download A Short Course in Differential Geometry and Topology PDF

Similar differential geometry books

New PDF release: Connections, curvature and cohomology. Vol. III: Cohomology

Greub W. , Halperin S. , James S Van Stone. Connections, Curvature and Cohomology (AP Pr, 1975)(ISBN 0123027039)(O)(617s)

Differential Geometry and Mathematical Physics: Part I. by Rudolph, G. and Schmidt, M. PDF

Ranging from undergraduate point, this e-book systematically develops the fundamentals of - research on manifolds, Lie teams and G-manifolds (including equivariant dynamics) - Symplectic algebra and geometry, Hamiltonian structures, symmetries and aid, - Integrable platforms, Hamilton-Jacobi concept (including Morse households, the Maslov category and caustics).

A treatise on the geometry of surfaces by Alfred Barnard Basset PDF

This quantity is made out of electronic photographs from the Cornell collage Library ancient arithmetic Monographs assortment.

Download PDF by Peter Petersen (auth.): Riemannian Geometry

Meant for a twelve months direction, this article serves as a unmarried resource, introducing readers to the real concepts and theorems, whereas additionally containing adequate history on complicated subject matters to entice these scholars wishing to concentrate on Riemannian geometry. this can be one of many few Works to mix either the geometric elements of Riemannian geometry and the analytic facets of the idea.

Additional info for A Short Course in Differential Geometry and Topology

Example text

10 (Fixed Points) Let G be a k-group scheme and M a G-module. Set (1) M G = { m ~ M I g ( m O 1 ) = m O 1 forall g E G ( A ) andall A } . This is a k-submodule of M and its elements are called the fixedpoints of G on M . If we take g = id,[,] E G(k[G]) in (l), then we get (2) M G = { m e MlA,(m) = m @ l } . 34 Representations of Algebraic Groups This description of M Gas kernel of AM - idMQ 1 yields (3) Let k' be a k-algebra which is flat as a k-module. Then (M Q k')Gk' = M G Q k'. In case k is a field, this implies, of course, = (MG),.

X G, ( n factors) and k[M,] with the polynomial ring k[T,, T',. . ,T,]. The multiplicatioe group over k is the k-group functor G, with G,(A) = A" = {units of A ) for all A. It is an algebraic k-group with k[G,] = k[T, 7-11. Any k-module M defines a k-group functor G L ( M ) with G L ( M ) ( A )= (End,(M 0A))" called the general linear group of M. In case M = k", we may identify G L ( M ) with GL, where G L , ( A ) is the group of all invertible (n x n)-matrices over A . Obviously, GL, is an algebraic k-group with k[GL,] isomorphic to the localization of the polynomial ring k [ q j , 1 Ii, j In] with respect to {(det)"I n E N}.

9). In the case where our ground ring k is a field we can be more precise. Then the injective G-modules are determined up to isomorphism by their socle and any semi-simple G-module M occurs as a socle of such an injective G-module; the injective hull of M . The indecomposable injective G-modules are just the injective hulls of the simple G-modules. We get especially a decomposition of k[G] generalizing the decomposition of the regular representation of a finite group into principal indecomposable modules.

Download PDF sample

A Short Course in Differential Geometry and Topology by A. T. Fomenko

by Charles
4.5

Rated 4.22 of 5 – based on 13 votes