Algebraic topology: a student's guide / J.F. Adams.

Format:

Book

Author/Creator:

Adams, J. Frank (John Frank), author.

Series:

London Mathematical Society lecture note series ; 4.

London Mathematical Society lecture note series ; 4

Language:

English

Subjects (All):

Algebraic topology.

Physical Description:

1 online resource (vi, 300 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1972.

Language Note:

English

Summary:

This set of notes, for graduate students who are specializing in algebraic topology, adopts a novel approach to the teaching of the subject. It begins with a survey of the most beneficial areas for study, with recommendations regarding the best written accounts of each topic. Because a number of the sources are rather inaccessible to students, the second part of the book comprises a collection of some of these classic expositions, from journals, lecture notes, theses and conference proceedings. They are connected by short explanatory passages written by Professor Adams, whose own contributions to this branch of mathematics are represented in the reprinted articles.

Contents:

Cover; Title; Copyright; Contents; Introduction; 1 A first course; 2 Categories and functors; 3 Semi-simplicial complexes; 4 Ordinary homology and cohomology; 5 Spectral sequences; 6 H*(BG); 7 Eilenberg-MacLane spaces and the Steenrod algebra; 8 Serrefs theory of classes of abelian groups (C-theory); 9 Obstruction theory; 10 Homotopy theory; 11 Fibre bundles and topology of groups; 12 Generalised cohomology theories; 13 Final touches; PAPERS ON ALGEBRAIC TOPOLOGY; 1; 1COMBINATORIAL HOMOTOPY; 4. Cell complexes.; 5. CW-complexes,; REFERENCES; 2; 2 AXIOMATIC APPROACH TO HOMOLOGY THEORY

1. Introduction2. Preliminaries; 3. Basic Concepts; 4. Axioms; 6. Existence; 7. Generalizations; 3&4; 3 LA SUITE SPECTRALE. I: CONSTRUCTION GENERALE; 1. Fondations; 2. Les suite f ondamentales; 3. Le cas gradue; 4. Le cas contravariant; 5. Le cas algebrique; 4 EXACT COUPLES IN ALGEBRAIC TOPOLOGY; Introduction; 1. Differential Groups; 2. Graded and Bigraded Groups; 3. Definition of a Leray-Koszul Sequence; 4. Definition of an Exact Couple; The Derived Couple; 5. Maps of Exact Couples; 6. Bigraded Exact Couples; The Associated Leray-Koszul Sequence; BIBLIOGRAPHY; 5

5 THE COHOMOLOGY OF CLASSIFYING SPACES OF tf-SPACES6; 6 Cohomologie modulo 2 des complexes d'Eilenberg-MacLane; Introduction; 1. PrGlirninaires; 2. Determination de Palgfcbre #*(77; q,Z2); 4. Operations cohomologiques; BIBLIOGRAPHIE; 7; 7 ON THE TRIAD CONNECTIVITY THEOREM; 8&9; 8 ON THE FREUDENTHAL THEOREMS; 1. Introduction; BIBLIOGRAPHY; 9 THE SUSPENSION TRIAD OF A SPHERE; 1. Introduction; BIBLIOGRAPHY; 10; 10 ON THE CONSTRUCTION FK; 1. Introduction; 2. The construction; 3. A theorem of Hilton; References; 11; 11ON CHERN CHARACTERS AND THE STRUCTURE OF THEUNITARY GROUP; 12; 13

13 GENERALISED HOMOLOGY AND COHOMOLOGY THEORIES14; 14 Matematisk Institut, Aarhus Universitet; 1. Homology theories; 2. h-fibrations and their spectral sequence; 3. The case π = id: B - B; 4. Multiplicative cohomology theories; REFERENCES; 15,16&17; 15 ON AXIOMATIC HOMOLOGY THEORY; 16CHARACTERS AND COHOMOLOGY OF FINITE GROUPS; 3. Inverse limits and completions.; 17EXTRACT FROM THESIS; 18; 18 RELATIONS BETWEEN COHOMOLOGY THEORIES; Poincare duality; REFERENCES; 19,20,21 &22; 19VECTOR BUNDLES AND HOMOGENEOUS SPACES; 1. A cohomology theory derived from the unitary groups.

2. The spectral sequence.3. The differentiable Riemann-Roch theorem and some applications.; 4. The classifying space of a compact connected Lie group.; REFERENCES; 20 LECTURES ON K-THEORY; 1. Vector bundles on X and vector bundles on X x S; 2. Definition of K(X); 3. Proof of Bott periodicity; 4. Elements of Hopf invariant one; 21 VECTOR FIELDS ON SPHERES; 22 ON THE GROUPS J(X)-IV; 1. INTRODUCTION; 2. COF1BERINGS; 3. DEFINITION AND ELEMENTARY PROPERTIES OF THE INVARIANTS d, e; 12. EXAMPLES; REFERENCES; 23; 23A SUMMARY ON COMPLEX COBORDISM; 24

24NEW IDEAS IN ALGEBRAIC TOPOLOGY(K-THEORY AND ITS APPLICATIONS)

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographies.

ISBN:

1-139-88358-5

1-107-36568-6

1-107-37042-6

1-107-36077-3

1-107-36827-8

1-299-40350-6

1-107-36322-5

0-511-66258-0