Cycles and spectra (Q1416093)

This is a survey on recent work on spaces of algebraic cycles, focusing on spaces of real and quaternionic cycles and their relation to equivariant Eilenberg-MacLane spaces. The main theme is connected to the principle according to which algebraic cycles constitute natural models for classifying spaces in topology. In turn this tells much about spaces of cycles. Most of the results discussed here are due to Pedro dos Santos, Paulo Lima-Filho, Marie-Louise Michelsohn and H. Blaine Lawson. This well written paper emphasizes the main results and ideas through a large number of examples. The paper is dedicated to IMPA on the occasion of its fiftieth anniversary.