Cartan and Eilenberg introduce the concept of homology in abstract algebra and algebraic topology. Their text provides a rigorous treatment of the theory and applications of homological algebra, including chain complexes, cohomology, and spectral sequences.
From the Preface: “There are three volumes. The first one contains a curriculum vitae, a «Brève Analyse des Travaux» and a Iist of publications, including books and seminars. In addition the volume contains all papers of H. Cartan on analytic functions published before 1939. The other papers on analytic functions, e. g. those on Stein manifolds and coherent sheaves, make up the second volume. The third volume contains, with a few exceptions, all further papers of H. Cartan; among them is a reproduction of exposés 2 to 11 of his 1954/55 Seminar on Eilenberg-MacLane algebras. Each volume is arranged in chronological order. The reader should be aware that these volumes do not fully reflect H. Cartan's work, a large part of which is also contained in his fifteen ENS-Seminars (1948-1964) and in his book „Homological Algebra“ with S. Eilenberg... Still, we trust that mathematicians throughout the world will welcome the availability of the „Oeuvres“ of a mathematician whose writing and teaching has had such an influence on our generation.”
From the Preface: “There are three volumes. The first one contains a curriculum vitae, a «Brève Analyse des Travaux» and a Iist of publications, including books and seminars. In addition the volume contains all papers of H. Cartan on analytic functions published before 1939. The other papers on analytic functions, e. g. those on Stein manifolds and coherent sheaves, make up the second volume. The third volume contains, with a few exceptions, all further papers of H. Cartan; among them is a reproduction of exposés 2 to 11 of his 1954/55 Seminar on Eilenberg-MacLane algebras. Each volume is arranged in chronological order. The reader should be aware that these volumes do not fully reflect H. Cartan's work, a large part of which is also contained in his fifteen ENS-Seminars (1948-1964) and in his book „Homological Algebra“ with S. Eilenberg... Still, we trust that mathematicians throughout the world will welcome the availability of the „Oeuvres“ of a mathematician whose writing and teaching has had such an influence on our generation.”
Addressed to 2nd- and 3rd-year students, this work by a world-famous teacher skillfully spans the pure and applied branches, so that applied aspects gain in rigor while pure mathematics loses none of its dignity. Equally essential as a text, a reference, or simply as a brilliant mathematical exercise. 1971 edition.
Basic treatment of the theory of analytic functions of a complex variable, touching on analytic functions of several real or complex variables as well as the existence theorem for solutions of differential systems where data is analytic. Also included is a theory of abstract complex manifolds of one complex dimension; holomorphic functions; Cauchy's integral, more. Exercises. 1973 edition.
InhaltsverzeichnisBegrüßungsansprache.Einführung in das Fest-Kolloquium zum 150. Geburtstag von Karl Weierstraß.Über den Vorbereitungssatz von Weierstraß.Elliptische Differentialoperatoren auf Mannigfaltigkeiten.
