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.

Show description

Read or Download Algebraic Topology: An Intuitive Approach PDF

Best topology books

Arthur Engel's Geometry Revisited PDF

This can be a arithmetic ebook, no longer a programming booklet, even though it explains Pascal to novices. it truly is aimed toward highschool scholars and undergraduates with a robust curiosity in arithmetic, and academics searching for clean rules. it really is choked with varied mathematical principles requiring little historical past. It incorporates a huge variety of not easy difficulties, a lot of which illustrate how numerical computation ends up in conjectures that could then be proved via mathematical reasoning.

Read e-book online Absolute Measurable Spaces (Encyclopedia of Mathematics and PDF

Absolute measurable house and absolute null house are very outdated topological notions, built from famous proof of descriptive set idea, topology, Borel degree concept and research. This monograph systematically develops and returns to the topological and geometrical origins of those notions. Motivating the improvement of the exposition are the motion of the gang of homeomorphisms of an area on Borel measures, the Oxtoby-Ulam theorem on Lebesgue-like measures at the unit dice, and the extensions of this theorem to many different topological areas.

New PDF release: Ordering Braids (Mathematical Surveys and Monographs)

Within the fifteen years because the discovery that Artin's braid teams get pleasure from a left-invariant linear ordering, a number of particularly various methods were used to appreciate this phenomenon. This booklet is an account of these ways, which contain such various gadgets and domain names as combinatorial workforce thought, self-distributive algebra, finite combinatorics, automata, low-dimensional topology, mapping classification teams, and hyperbolic geometry.

Read e-book online Topologie Générale: Chapitres 5 à 10 PDF

Topologie générale, Chapitres five � 10Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce deuxième quantity du Livre de Topologie générale, troisième Livre du traité, décrit de nombreux outils fondamentaux en topologie et en examine, tels que le théorème d’Urysohn, le théorème de Baire ou les espaces polonais.

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.

Download PDF sample

Algebraic Topology: An Intuitive Approach by Hajime Sato


by Joseph
4.0

Rated 4.24 of 5 – based on 35 votes