Topology

Locally semialgebraic spaces serve as an appropriateframework for studying the topological properties ofvarieties and semialgebraic sets over a real closed field.

The main purpose of part I of these notes is to develop for a ring R a functional notion of R-completion of a space X.

From the Preface by D.

Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field.