Heinz Hopf Livres

Heinz Hopf's contributions to modern mathematics are profound and diverse, encompassing areas such as homological algebra, global differential geometry, and the algebraization of topology. His work, though limited to around 70 writings, has significantly influenced various fields, including group theory, analysis, and algebraic geometry. The clarity and accessibility of his writing, along with the concrete problems he addressed, highlight the depth and reach of his innovative methods, making his legacy a cornerstone of contemporary mathematical thought.

Das Buch ist Teil des Digitalisierungsprojekts des Springer Book Archives, das historische Publikationen seit 1842 umfasst. Es bietet wertvolle Quellen für die historische und disziplingeschichtliche Forschung, die im jeweiligen historischen Kontext analysiert werden sollten. Da der Titel vor 1945 veröffentlicht wurde, wird seine politisch-ideologische Ausrichtung nicht beworben, was auf die Sensibilität der Inhalte hinweist.

From the preface: „Hopf algebras, Hopf fibration of spheres, Hopf-Rinow complete Riemannian manifolds, Hopf theorem on the ends of groups - can one imagine modern mathematics without all this? Many other concepts and methods, fundamental in various mathematical disciplines, also go back directly or indirectly to the work of Heinz Hopf: homological algebra, singularities of vector fields and characteristic classes, group-like spaces, global differential geometry, and the whole algebraisation of topology with its influence on group theory, analysis and algebraic geometry. It is astonishing to realize that this oeuvre of a whole scientific life consists of only about 70 writings. Astonishing also the transparent and clear style, the concreteness of the problems, and how abstract and far-reaching the methods Hopf invented.“