# Contents

## Idea

Every spectrum $K$ is the coefficient object of a generalized cohomology theory and dually of a generalized homology theory.

For $K = H R$ an Eilenberg-MacLane spectrum this reduces to ordinary homology

## References

Original articles include

• Friedrich Bauer, Classifying spectra for generalized homology theories Annali di Maternatica pura ed applicata (IV), Vol. CLXIV (1993), pp. 365-399

• Friedrich Bauer, Remarks on universal coefficient theorems for generalized homology theories Quaestiones Mathematicae Volume 9, Issue 1 & 4, 1986, Pages 29 - 54

A general construction of homologies by “geometric cycles” similar to the Baum-Douglas geometric cycles for K-homology is discussed in

• S. Buoncristiano, C. P. Rourke and B. J. Sanderson, A geometric approach to homology theory, Cambridge Univ. Press, Cambridge, Mass. (1976)

Further generalization of this to bivariant cohomology theories is in

• Martin Jakob, Bivariant theories for smooth manifolds, Applied Categorical Structures 10 no. 3 (2002)

Revised on February 23, 2014 03:15:57 by Urs Schreiber (77.80.20.34)