Synopses & Reviews
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 these, and other, areas. The surveys are exemplary in the way they make difficult mathematical ideas easily comprehensible and accessible even to non-specialists. The topics treated here can be classed in 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 has since been emeritus professor.
Synopsis
Zur Homotopietheorie gefaserter R ume.- ber die Homotopiegruppen von Gruppenr umen.- Systeme von Richtungsfeldern in Sph ren und stetige L sungen komplexer linearer Gleichungen.- L'id e de dimension.- Stetige L sungen linearer Gleichungssysteme.- Gruppentheoretischer Beweis des Satzes von Hurwitz-Radon ber die Komposition quadratischer Formen.- Topologie und Algebra.- ber monothetische Gruppen.- Harmonische Funktionen und Randwertaufgaben in einem Komplex.- Der Cohomologie-Ring einer beliebigen Gruppe.- Coverings and Betti numbers.- Formes diff rentielles et m trique hermitienne sans torsion. I. Structure complexe, formes pures.- Formes diff rentielles et m trique hermitienne sans torsion. II. Formes de classe k; formes analytiques.- Sur les vari t s closes m trique hermitienne sans torsion.- Quelques propri t s globales des vari t s k hl riennes.- Espaces fibr s et homotopie.- Sur l'int grabilit des structures presque complexes.- Complex-analytic manifolds.- On complexes with operators.- ber injektive Moduln.- Cohomology of groups and transfer.- A class of compact, complex manifolds which are not algebraic.- Structures complexes et transformations infinit simales.- R ume mit Mittelbildungen.- Zur Cohomologietheorie von R umen und Gruppen.- Homotopie et dualit .- Groupes d'homotopie et dualit . Groupes absolus.- Groupes d'homotopie et dualit . Suites exactes.- Groupes d'homotopie et dualit . Coefficients.- Transgression homotopique et cohomologique.- D composition homologique d'un poly dre simplement connexe.- On the homology and homotopy decomposition of continuous maps.- Groupes d'homotopie et dualit .- Structure maps in group theory.- Group-like structures in general categories I. Multiplications and comultiplications.- 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 poly dre.- 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 Poincar duality.- Finiteness properties of duality groups.- Aspherical manifolds and higher-dimensional knots.- Cobordism for Poincar duality groups.- Rational representations of finite groups and their Euler class.- Two-dimensional Poincar 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).- Poincar duality groups of dimension two.- Chern classes of group representations over a number field.- Plane motion groups and virtual Poincar duality of dimension two.- Poincar 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.- Poincar 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 of groups.- IV. Homological algebra, transfer.- V. Duality in homotopy theory.- VI. Duality groups, Poincar duality.- Bibliography of the publications of B. Eckmann.- List of Ph.D. Theses written under the supervision of B. Eckmann.
About the Author
Prof. Beno Eckmann (1917-2008) was a distinguished mathematician who also exerted great influence on the promotion and development of Mathematics all over the globe. At Ben Gurion University he initiated the establishment of the Center for Advanced Studies in Mathematics, and served actively on its advisory committee until his passing away. Prof. Eckmann studied at ETH, where his PhD advisor was the famous Heinz Hopf. His brilliant Ph.D. work won him the Kern Prize and silver medal. He was a member of the Institute for Advanced Study in Princeton in 1947, 1951 and 1952, where he worked with Albert Einstein and John von Neumann. Prof. Eckmann is considered one of the founding fathers of Homological Algebra and Category Theory, with special emphasis on Topology and Cohomology of Groups. A close cooperation between Eckmann and Peter Hilton, who was a frequent guest at ETH since the 1950's, led to numerous papers (over 25) on these subjects. Eckmann had over 60 Ph.D. students, many of whom also became prominent mathematicians. In parallel with his scientific endeavors, Prof. Eckmann contributed significantly to the promotion and development of Mathematics, often through his ability to convince others of the importance of the field. For example, in 1964 he established the famous Institute for Advanced Studies at ETH, which he headed for 20 years until his retirement. Later he interested the Springer family, through Julius Springer, to establish the prestigious and influential series "Lecture Notes in Mathematics". He was the chief editor of this series until near his passing away. He was awarded many honorary degrees, one of them from Ben Gurion University. He was president of the Swiss Mathematical Society and secretary of the International Mathematical Union for 5 years. He also served as an Honorary President of the International Congress of Mathematicians in Zurich in 1994.
Table of Contents
Curriculum vitae.- Biographical note.- 64 papers from Beno Eckmann.- Notes.- Bibliography of the publications of Beno Eckmann.- List of Ph.D. Theses written under the supervision of B. Eckmann.