توپولوژی گروه‌های لی، جلد اول و دوم

This translation of a Japanese 2 volume set on the topology of Lie groups covers many topics in algebraic topology, such as homology theory and stable homotopy, and geometry, such as vector bundles, and uses them to calculate the topological properties of Lie groups. While it defines many elementary concepts, such as that of a Lie group or a vector bundle, it barely explains anything. Theorems are stated, but rarely proved; instead, the authors in the foreward claim that the reader should be able to supply the proofs, as if the readers could develop the entire machinery of algebraic topology on their own. Occasionally results are proved, but only easy ones, as if the authors are just being lazy. Definitely no one could actually learn any topology from this book, but rather than just admitting this and assuming that the reader has the background, many basic concepts are defined and elementary theorems are stated, which just serves to waste space. The only real value of this book is that it collects in one place many useful and interesting facts about Lie groups, which is why I said it was encyclopedic. One could use it as a reference to look up the stable homotopy groups of classical Lie groups, for example, but not much more than that. One unusual feature of this book is that it also covers exceptional Lie groups, such as F4 or E8, which is pretty rare - offhand I can't think of any other book that gives algebraic topological facts on them. Two treatments of the topology of Lie groups for senior students of mathematics, as a supplemental bridge between linear algebra and the more specialized disciplines that use it. The first book progresses from linear algebra to the periodicity of KO-groups; the second continues from the theory of compact Lie groups to exceptional groups. No bibliography. Lie groups are very general mathematical objects that appear in numerous areas such as topology, functional analysis, and algebra, as well as differential geometry and differential topology. This book provides a guide to the topology of Lie groups and homogeneous spaces by bringing together a wide range of results relating to them.