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. The purpose of these two parts is to provide a guide to the topology of Lie groups and homogeneous spaces by bringing together a wide range of results relating to them. The first part thoroughly studies topological properties of the classical groups as typical examples of Lie groups. In the second part, the authors study general properties of compact Lie groups, particularly the exceptional groups.

Reviews

"The book could prove very useful for mathematicians or physicists interested in the basic topological and homotopy-theoretic aspects of Lie groups and their homogeneous space."

-- Mathematical Reviews

Table of Contents

• Classical groups
• Covering spaces and fibre bundles
• Cohomology groups of classical groups and their homogeneous spaces
• The periodicity of \(K\mathbf F\)-groups and the homotopy groups

• Compact Lie groups
• The Morse-Bott theory
• Cohomology of exceptional groups