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This volume contains research papers and survey articles written by Beno Eckmann from 1941 to the present day. 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.

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"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."

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