Chapter 11 - Introduction to Nonconnective Im(J)-Theory

Abstract

This chapter introduces nonconnective Im (J) - theory. Classical if-theory has many applications to geometry and homotopy theory, e.g., the e-invariant of Adams and Toda, the J-homomorphism, the J(X)-groups or v1-periodicity in stable homotopy. The purpose of this chapter is to give an introduction to /m(J)-theory, to supply elementary proofs for some basic properties of Ad-theory and to study some examples. The chapter begins with the definition of Ad as a cofibre spectrum. The chapter then describes its coefficient groups and introduces the Chern-Dold character for Ad-theory.