Analytic K-Homology

This text acquaints the reader with the essential ideas of analytic K-homology and develops some of its applications. It includes a detailed introduction to the necessary functional analysis, followed by an exploration of the connections between K-homology and operator theory, coarse geometry, index theory, and assembly maps, including a detailed treatment of the Atiyah-Singer Index Theorem. Beginning with the rudiments of C*-algebra theory, it leads the reader into some of the central notions of contemporary research in geometric functional analysis.

Nigel Higson is at Pennsylvania State University. John Roe is at Pennsylvania State University.