By Jean Dieudonné

Written by way of a world-renowned mathematician, this good proficient and vintage textual content strains the background of algebraic topology, starting with its production within the early 1900s. It is going directly to describe intimately the $64000 theories that have been came upon prior to 1960.

**Read or Download A History of Algebraic and Differential Topology (1900 - 1960) PDF**

**Similar differential geometry books**

**Compact Riemann Surfaces: An Introduction to Contemporary Mathematics**

Even if Riemann surfaces are a time-honoured box, this publication is novel in its extensive standpoint that systematically explores the relationship with different fields of arithmetic. it might function an creation to modern arithmetic as a complete because it develops historical past fabric from algebraic topology, differential geometry, the calculus of adaptations, elliptic PDE, and algebraic geometry.

**The geometry of physics: An introduction**

This e-book offers a operating wisdom of these elements of external differential varieties, differential geometry, algebraic and differential topology, Lie teams, vector bundles, and Chern varieties which are worthwhile for a deeper knowing of either classical and sleek physics and engineering. it really is perfect for graduate and complicated undergraduate scholars of physics, engineering or arithmetic as a direction textual content or for self learn.

**Noncommutative Geometry, Quantum Fields and Motives**

The unifying topic of this ebook is the interaction between noncommutative geometry, physics, and quantity idea. the 2 major gadgets of research are areas the place either the noncommutative and the motivic features come to play a job: space-time, the place the guideline is the matter of constructing a quantum idea of gravity, and the distance of primes, the place you can still regard the Riemann speculation as a long-standing challenge motivating the advance of recent geometric instruments.

**Geometry, Analysis and Dynamics on Sub-riemannian Manifolds**

A ebook of the ecu Mathematical Society Sub-Riemannian manifolds version media with restricted dynamics: movement at any aspect is permitted merely alongside a constrained set of instructions, that are prescribed by means of the actual challenge. From the theoretical standpoint, sub-Riemannian geometry is the geometry underlying the speculation of hypoelliptic operators and degenerate diffusions on manifolds.

- Involutive Hyperbolic Differential Systems
- Lie algebras, geometry and Toda-type systems
- Manifolds, Sheaves, and Cohomology
- Algorithmic and Computer Methods for Three-Manifolds

**Extra resources for A History of Algebraic and Differential Topology (1900 - 1960)**

**Example text**

2). Explicit formulas for Q6 and Q8 in terms of Riemannian invariants were derived in [116]. The complexity of such formulas increases exponentially with the order. It is one purpose of the present book to reveal the structure of these quantities. 5 to deﬁne the so-called residue families. These families will be used to study the structure of Q-curvatures. 5. The relation of residue families to GJMS-operators and Q-curvature is as follows. For any metric h on M n and any integer N ∈ [1, n2 ], there is a residue 22 Chapter 1.

But holomorphy of Mu (λ), ϕ on C is lost for test functions ϕ ∈ C ∞ (S n ) the support of which intersects with S n−1 . However, thanks to the controlled boundary behaviour of u in terms of its asymptotics, the family Mu (λ) admits a meromorphic continuation to C as a family of distributions. In order to study the continuation, we write 1 ρλ+μ+N Mu (λ), ϕ = N ≥0 S n−1 0 aN (f )(x)ϕ(ρ, x)dx (1−ρ2) n−2 2 dρ 1 ρλ+n−1−μ+N + N ≥0 S n−1 0 bN (f )(x)ϕ(ρ, x)dx (1−ρ2 ) n−2 2 dρ. n−2 Using a Taylor series for (1 − ρ2 ) 2 , and repeated partial integration in ρ, we construct a meromorphic continuation of Mu (λ) with simple poles in the disjoint ladders λ ∈ −μ−1−N0, λ ∈ −(n−1−μ)−1−N0.

N ≥0 The eigenfunction u gives rise to a holomorphic family of measures on the halfplane (λ) > −(n−1)/2 by Mu (λ), ϕ = H+ H0λ uϕdb, ϕ ∈ C ∞ (S n ). The support of these measures is contained in H + . Moreover, the restriction of Mu (λ) to the open H + can be identiﬁed with the holomorphic family of functions λ → H0λ u. But holomorphy of Mu (λ), ϕ on C is lost for test functions ϕ ∈ C ∞ (S n ) the support of which intersects with S n−1 . However, thanks to the controlled boundary behaviour of u in terms of its asymptotics, the family Mu (λ) admits a meromorphic continuation to C as a family of distributions.