Akadémiai Kiadó

      The volume gives an exposition to an axiomatic approach to the idea of linking.       The axiomatization of the homology theory due to Eilenberg and Steenrod (Eilenberg, S., Steenrod, N., Foundations of Algebraic Topology, Princeton 1952) raises a new problem, namely to develop a uniform theory of linking of homology theories applied to singular homology theories as well as to Čech homology theories and any other homology theories. This problem is examined in the present volume.       Some geometric applications are also presented; in particular, the Decomposition Theorem (Alexandrov's "Zerlengungssatz") and a few related theorems.       Although the book does not presuppose any preliminary knowledge, it is mainly suggested to readers who are familiar with Eilenberg-Steenrod's axiomatic foundation of the homology theory.       Contents: Preface. Introduction. Basic notations. Fundamental properties of the linking theory. Proof of the uniqueness theorem of the small linking theory. Proof of the existence theorem of the small linking theory. Big linking theory. p-linking theories. Geometric applications. Bibliography. List of symbols. Subject Index.       Mátyás Bognár is Professor of Mathematics at Eötvös Loránd University in Budapest, Hungary. He received the degree Doctor of Sciences in 1970. He has published over thirty research papers in the field of algebraic and general topology, theory of discrete and topological Abelian groups, category theory, geometry, theory of graphs and measure theory. Actually he is also external research fellow of the Mathematical Institute of the Hungarian Academy of Sciences.