Download Algebraic Topology via Differential Geometry by M. Karoubi, C. Leruste PDF

By M. Karoubi, C. Leruste

During this quantity the authors search to demonstrate how equipment of differential geometry locate software within the research of the topology of differential manifolds. must haves are few because the authors take pains to set out the idea of differential varieties and the algebra required. The reader is brought to De Rham cohomology, and specific and special calculations are current as examples. subject matters lined comprise Mayer-Vietoris detailed sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This booklet should be compatible for graduate scholars taking classes in algebraic topology and in differential topology. Mathematicians learning relativity and mathematical physics will locate this a useful advent to the strategies of differential geometry.

Show description

Read or Download Algebraic Topology via Differential Geometry PDF

Best differential geometry books

Compact Riemann Surfaces: An Introduction to Contemporary Mathematics

Even supposing Riemann surfaces are a time-honoured box, this publication is novel in its vast viewpoint that systematically explores the relationship with different fields of arithmetic. it could actually function an creation to modern arithmetic as an entire because it develops history fabric from algebraic topology, differential geometry, the calculus of adaptations, elliptic PDE, and algebraic geometry.

The geometry of physics: An introduction

This booklet presents a operating wisdom of these elements of external differential types, differential geometry, algebraic and differential topology, Lie teams, vector bundles, and Chern varieties which are useful for a deeper figuring out of either classical and glossy physics and engineering. it truly is excellent for graduate and complex 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 booklet is the interaction between noncommutative geometry, physics, and quantity concept. 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 thought of gravity, and the gap of primes, the place you could regard the Riemann speculation as a long-standing challenge motivating the improvement of latest geometric instruments.

Geometry, Analysis and Dynamics on Sub-riemannian Manifolds

A booklet of the eu Mathematical Society Sub-Riemannian manifolds version media with limited dynamics: movement at any element is authorized basically alongside a constrained set of instructions, that are prescribed by way of the actual challenge. From the theoretical viewpoint, sub-Riemannian geometry is the geometry underlying the idea of hypoelliptic operators and degenerate diffusions on manifolds.

Extra resources for Algebraic Topology via Differential Geometry

Example text

For all 13 column. • Thus l < 3 < n M eU. ID To go further in the same direction, one is led to introduce matrices of differential forms each coefficient of which is an element of * ft (U) . F o ran example, in ft (U) notation. t h ematrix will be denoted by (dx. ) . , . , . . , i ] 1 < l < n, 1 < ] < n with dM in conformity with the usual abuse of * M (ft (U) ) , The result i s an It-algebra: the matrix algebra M (0) n for short. k Note that i t is graded by the subspaces in ft (U), + Mn (U) , derived from that i s analogous to the multiplication of 'ordinary' matrices, except that the, product of differential forms obviously remains a n t i - commutative.

S k - 1 , d and 6 coincide as 1 < deg Y. 7) . Then because of ( i i ) and ( i i i ) for a l l i in 39 da = 2, d ( B i i A Y±) I (dSi A Tj, + ( - l ) d e g 6 i Si A dYi) . i A similar expression i s obtained for 6a, hence da = 6a on O £2 (U) . by induction hypothesis. II Existence Condition If a = I a dx (v) d e f i n e s e Q (U) , d where a efJ°(U), set n da= (cf. Y , d a A d x = L -jk. I I I e J n Y da. ^ . I ,. l < i , < . . < i,

Thus l < 3 < n M eU. ID To go further in the same direction, one is led to introduce matrices of differential forms each coefficient of which is an element of * ft (U) . F o ran example, in ft (U) notation. t h ematrix will be denoted by (dx. ) . , . , . . , i ] 1 < l < n, 1 < ] < n with dM in conformity with the usual abuse of * M (ft (U) ) , The result i s an It-algebra: the matrix algebra M (0) n for short. k Note that i t is graded by the subspaces in ft (U), + Mn (U) , derived from that i s analogous to the multiplication of 'ordinary' matrices, except that the, product of differential forms obviously remains a n t i - commutative.

Download PDF sample

Rated 4.48 of 5 – based on 37 votes