TL;DR
This paper provides a comprehensive introduction to K-Theory, covering its main branches—topological, analytic, and algebraic—with detailed lectures suitable for graduate students.
Contribution
It offers a structured, accessible set of lectures that synthesize foundational concepts across all three major branches of K-Theory, based on a well-organized summer school curriculum.
Findings
Clear exposition of topological K-Theory
Introduction to analytic K-Homology concepts
Overview of higher algebraic K-Theory
Abstract
We present 18 Introductory Lectures on K-Theory covering its basic three branches, namely topological, analytic (K-Homology) and Higher Algebraic K-Theory, 6 lectures on each branch. The skeleton of these notes was provided by the author's personal notes from a graduate summer school on K-Theory organised by the London Mathematical Society (LMS) back in 1995 in Lancaster, UK.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Advanced Operator Algebra Research