Download PDF by Hajime Sato: Algebraic Topology: An Intuitive Approach

By Hajime Sato

ISBN-10: 0821810464

ISBN-13: 9780821810460

The only so much tricky factor one faces whilst one starts to profit a brand new department of arithmetic is to get a believe for the mathematical feel of the topic. the aim of this e-book is to aid the aspiring reader gather this crucial logic approximately algebraic topology in a quick time period. To this finish, Sato leads the reader via uncomplicated yet significant examples in concrete phrases. in addition, effects aren't mentioned of their maximum attainable generality, yet when it comes to the best and such a lot crucial instances.

In reaction to feedback from readers of the unique version of this booklet, Sato has further an appendix of important definitions and effects on units, common topology, teams and such. He has additionally supplied references.

Topics lined contain primary notions akin to homeomorphisms, homotopy equivalence, basic teams and better homotopy teams, homology and cohomology, fiber bundles, spectral sequences and attribute periods. gadgets and examples thought of within the textual content contain the torus, the Möbius strip, the Klein bottle, closed surfaces, mobile complexes and vector bundles.

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Additional info for Algebraic Topology: An Intuitive Approach

Sample text

3. Corps des fractions d’un anneau strictement local . . . . . . . 4. Dimension cohomologique : cas inversible dans OX . . . . . 5. Dimension cohomologique : cas = p . . . . . . . . . . . . . 6. Dimension cohomologique pour un préschéma de type fini sur Spec Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . Références . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 31 32 36 38 40 42 44 1. Introduction 43 Dans cet exposé on convient, sauf mention expresse du contraire, que « faisceau » signifie « faisceau abélien ».

Hq (Scl , fcl∗ F) −→ Hq (Xcl , F) −→ Hq−1 (Scl , R1 fcl∗ F) −→ Soit s l’image de x dans S. Par hypothèse de récurrence et grâce à (i), il existe pour chaque classe η ∈ Hq (Scl , G) (G localement constant de torsion, à fibres finies) un « voisinage étale » S → S de s tel que l’image de η dans Hq (Scl , G) soit nul. Or les foncteurs Rq fcl∗ commutent évidemment aux changements de base étales, et si S → S est un voisinage étale de s, alors X = X × S → X est un voisinage étale de x. Lorsque S q 1 on termine donc grâce à la suite exacte (∗) en prenant d’abord G = R1 fcl∗ F et ensuite G = fcl∗ F.

31 31 32 36 38 40 42 44 1. Introduction 43 Dans cet exposé on convient, sauf mention expresse du contraire, que « faisceau » signifie « faisceau abélien ». Soient X un schéma et ∈ P. « Rappelons » qu’on appelle -dimension cohomologique de X le plus grand entier cd X = n (ou = ∞ si ce nombre n’existe pas) tel que Hn (X, F) = 0 pour au moins un faisceau de -torsion F sur X. Si X = Spec A, nous écrivons cd A = cd Spec A. Tenant compte du dictionnaire (VIII 2) on retrouve ainsi la notion « classique » de [CG] dans le cas où A = k est un corps.

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Algebraic Topology: An Intuitive Approach by Hajime Sato

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