Ebook: Homology of classical groups over finite fields, associated infinite loop spaces

One of Che hallmarks of significant advances in mathematics is the discovery of unexpected relationships between diverse areas. Perhaps the most notable recent example of such an advance is D« Quillen!s development of higher algebraic K-theory in which algebra and topology are related in a new and fundamental way. On the one hand higher algebraic K-theory introduces topological methods for defining algebraic invariants, such as the higher K-groups of rings. On the other it provides a machine for translating algebraic concepts into topological concepts.