Hopf, H: Collected Papers - Gesammelte Abhandlungen

Table of Contents.- List of Publications of Heinz Hopf.- Editor's Preface.- Papers of Heinz Hopf.- Heinz Hopf Selecta.

Heinz Hopf (1894-1981) is rightly considered to be one of the outstanding and most influential mathematicians of the XXth century. He was a pioneer in algebraic topology as well as in differential geometry. He is widely known as having studied the 'Hopf fibration'. The very general abstract notion of Hopf algebra was introduced as tracing in Hopf's works; he may be considered to have been a forerunner of the creation of homological algebra. He found a noncontractible map of the 3-sphere into the 2-sphere; that result was an essential step towards the concept of 'Hopf invariant' and the popularization of the homotopy group notion due to Hurewicz.

Heinz Hopf was born in Wroclaw (Breslau), in the then German part of Poland. He studied in his home town, in Heidelberg and in Berlin, visited Göttingen, Princeton University, and finally settled at ETH in Zürich, where he became Weyl's successor.

The Heinz Hopf Selecta published in 1964 contained an important - although far from being complete - part of Hopf's mathematical production. So this volume presenting Hopf's collected works is welcome. As one may expect, the organisational achievement by Beno Eckmann, Hopf's student and friend, is high class. Two important articles are translated from German into English.

This book of over 1200 pages featuring 71 items constitutes an essential reference for the development of mathematics during the XXth century.

Jean-Paul Pier (Zbl. MATH 980, 01027)