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Full Description
This volume contains research papers and survey articles written by Beno Eckmann from 1941 to 1986. The aim of the compilation is to provide a general view of the breadth of Eckmann's mathematical work. His influence was particularly strong in the development of many subfields of topology and algebra, where he repeatedly pointed out close, and often surprising, connections between them and other areas. The surveys are exemplary in terms of how they make difficult mathematical ideas easily comprehensible and accessible even to non-specialists. The topics treated here can be classified into the following, not entirely unrelated areas: algebraic topology (homotopy and homology theory), algebra, group theory and differential geometry. Beno Eckmann was Professor of Mathematics at the University of Lausanne, 1942-48, and Principal of the Institute for Mathematical Research at the ETH Zurich, 1964-84, where he was therefore an emeritus professor.
Contents
Zur Homotopietheorie gefaserter Räume.- Über die Homotopiegruppen von Gruppenräumen.- Systeme von Richtungsfeldern in Sphären und stetige Lösungen komplexer linearer Gleichungen.- L'idée de dimension.- Stetige Lösungen linearer Gleichungssysteme.- Gruppentheoretischer Beweis des Satzes von Hurwitz-Radon über die Komposition quadratischer Formen.- Topologie und Algebra.- Über monothetische Gruppen.- Harmonische Funktionen und Randwertaufgaben in einem Komplex.- Der Cohomologie-Ring einer beliebigen Gruppe.- Coverings and Betti numbers.- Formes différentielles et métrique hermitienne sans torsion. I. Structure complexe, formes pures.- Formes différentielles et métrique hermitienne sans torsion. II. Formes de classe k; formes analytiques.- Sur les variétés closes à métrique hermitienne sans torsion.- Quelques propriétés globales des variétés kählériennes.- Espaces fibrés et homotopie.- Sur l'intégrabilité des structures presque complexes.- Complex-analytic manifolds.- On complexes with operators.- Über injektive Moduln.- Cohomology of groups and transfer.- A class of compact, complex manifolds which are not algebraic.- Structures complexes et transformations infinitésimales.- Räume mit Mittelbildungen.- Zur Cohomologietheorie von Räumen und Gruppen.- Homotopie et dualité.- Groupes d'homotopie et dualité. Groupes absolus.- Groupes d'homotopie et dualité. Suites exactes.- Groupes d'homotopie et dualité. Coefficients.- Transgression homotopique et cohomologique.- Décomposition homologique d'un polyèdre simplement connexe.- On the homology and homotopy decomposition of continuous maps.- Groupes d'homotopie et dualité.- Structure maps in group theory.- Group-like structures in general categories I. Multiplications andcomultiplications.- Homotopie und Homologie.- Generalized means.- Homotopy and cohomology theory.- Unions and intersections in homotopy theory.- Composition functors and spectral sequences.- Commuting limits with colimits.- Continuous solutions of linear equations — some exceptional dimensions in topology.- Le groupe des types simples d'homotopie sur un polyèdre.- Simple homotopy type and categories of fractions.- On central group extensions and homology.- On the homology theory of central group extensions: I — The commutator map and stem extensions.- On the Schur multiplicator of a central quotient of a direct product of groups.- Groups with homological duality generalizing Poincaré duality.- Finiteness properties of duality groups.- Aspherical manifolds and higher-dimensional knots.- Cobordism for Poincaré duality groups.- Rational representations of finite groups and their Euler class.- Two-dimensional Poincaré duality groups and pairs.- On the Euler class of representations of finite groups over real fields.- Some recent developments in the homology theory of groups (Groups of finite and virtually finite dimension).- Poincaré duality groups of dimension two.- Chern classes of group representations over a number field.- Plane motion groups and virtual Poincaré duality of dimension two.- Poincaré duality groups of dimension two, II.- Profinite Chern classes for group representations.- The p-periodicity of the groups GL (n, Os(K)) and SL(n, Os(K)).- Galois action on algebraic matrix groups, Chern classes and the Euler class.- Poincaré duality groups of dimension two are surface groups.- Cyclic homology of groups and the Bass conjecture.- Notes.- I. Homotopy groups and fiber spaces.- II. Continuous solutions of linear equations.- III. Cohomology ofgroups.- IV. Homological algebra, transfer.- V. Duality in homotopy theory.- VI. Duality groups, Poincaré duality.- Bibliography of the publications of B. Eckmann.- List of Ph.D. Theses written under the supervision of B. Eckmann.
