#k-theory

19. K-Theory

This volume studies algebraic and topological K-theory, focusing on invariants derived from vector bundles, modules, and operator algebras. It provides tools for classification problems across algebra, topology, and geometry. Part I. Foundations of K-Theory Chapter 1. Motivation and Basic Definitions 1.1 Classification problems 1.2 Grothendieck groups 1.3 Additive invariants 1.4 Exact sequences 1.5 Examples Chapter 2. Grothendieck Construction 2.1 Monoids to groups 2.2 Universal properties 2.3 Functoriality 2.4 Examples in...