Download A History Of Algebraic And Differential Topology, 1900-1960 by Jean Dieudonné PDF

By Jean Dieudonné

A vintage on hand back! This e-book strains the historical past of algebraic topology starting with its production via Henry Poincaré in 1900, and describing intimately the real rules brought within the conception earlier than 1960. In its first thirty years the sector appeared constrained to purposes in algebraic geometry, yet this replaced dramatically within the Nineteen Thirties with the production of differential topology through Georges De Rham and Elie Cartan and of homotopy thought through Witold Hurewicz and Heinz Hopf. The impression of topology started to unfold to an increasing number of branches because it steadily took on a important position in arithmetic. Written by means of a world-renowned mathematician, this ebook will make intriguing examining for somebody operating with topology.

Show description

Read or Download A History Of Algebraic And Differential Topology, 1900-1960 PDF

Best differential geometry books

Surveys in Differential Geometry: Papers dedicated to Atiyah, Bott, Hirzebruch, and Singer (The founders of the Index Theory) (International Press) (Vol 7)

The Surveys in Differential Geometry are supplementations to the magazine of Differential Geometry, that are released via overseas Press. They comprise major invited papers combining unique examine and overviews of the most up-tp-date study in particular parts of curiosity to the turning out to be magazine of Differential Geometry neighborhood.

Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics

Critical transforms, resembling the Laplace and Fourier transforms, were significant instruments in arithmetic for no less than centuries. within the final 3 many years the improvement of a couple of novel principles in algebraic geometry, classification conception, gauge concept, and string concept has been heavily concerning generalizations of indispensable transforms of a extra geometric personality.

Riemannsche Geometrie im Großen

Aus dem Vorwort: "Globale Probleme der Differentialgeometrie erfreuen sich eines immer noch wachsenden Interesses. Gerade in der Riemannschen Geometrie hat die Frage nach Beziehungen zwischen Riemannscher und topologischer Struktur in neuerer Zeit zu vielen sch? nen und ? berraschenden Einsichten gef?

Geometric analysis and function spaces

This publication brings into concentration the synergistic interplay among research and geometry through reading a number of subject matters in functionality idea, genuine research, harmonic research, a number of complicated variables, and crew activities. Krantz's technique is prompted through examples, either classical and glossy, which spotlight the symbiotic dating among research and geometry.

Extra info for A History Of Algebraic And Differential Topology, 1900-1960

Sample text

Thus V and R can be considered as instances of the Sent Venant operator. 4. 2 33 Each of these three operators has its own advantages. 1), as we shall see later. The operator R has the most of symmetries (which are similar to the symmetries of the curvature tensor [25]) and, consequently, is more appropriate for answering the question about a number of linearly independent equations in the system W f = 0. 17). jm−1 : (i1 . . im )(j1 . . 8) there exists a unique solution to the equation σ(i1 .

Im ) with respect to the index im . 1). jm = α(im jm ) σ(i1 . . im−1 ) σ(j1 . . im−1 . 2 For f ∈ C ∞ (S m ), the next relations are valid: 1 σ(i1 . . im ) σ(j1 . . jm . 5) 32 CHAPTER 2. THE RAY TRANSFORM ON EUCLIDEAN SPACE P r o o f. From the definition of V and the evident equality σ(i1 . . im ) σ(j1 . . jm ) α(im jm ) σ(i1 . . im−1 ) σ(j1 . . jm−1 ) = = σ(i1 . . im ) σ(j1 . . jm ) α(im jm ), we obtain m−1 1 m−1 σ(i1 . . im ) σ(j1 . . jm = σ(i1 . . im ) σ(j1 . . im . 4). Decomposing the symmetrizations σ(i1 .

9). The lemma is proved. 2 we need the next easy 34 CHAPTER 2. jq : i1 . . ip (j1 . . jq ). jk ) ∈ T p+k (k = 0, . . 12) has at most one solution z ∈ C q+1 (T p ; U ) satisfying the initial conditions ∇k z(x0 ) = z k (k = 0, 1, . . , q − 1). jq ; jq+1 : i1 . . ip (j1 . . jk : i1 . . ip (j1 . . jk ) (k = 0, 1, . . , q − 1). 13). jq : (i1 . . ip )(j1 . . jk : (i1 . . ip )(j1 . . jk ) (k = 0, 1, . . 13) belongs to C q+1 (S m ; U ). For p = 0, q = 1 the lemma is equivalent to the claim of necessity and (in the case of a simply-connected U ) sufficiency of the conditions ∂yi /∂xj = ∂yj /∂xi for integrability of the Pfaff form yi dxi .

Download PDF sample

Rated 4.96 of 5 – based on 40 votes