Topology

Abstract

This chapter focuses on the literature on topology. It focuses on use of the literature in two fields, which can broadly be described as follows: (1) classical, homotopy-invariant algebraic topology; and (2) its application to the study of manifolds. The former is a subject that enjoyed a period of rapid growth starting in the early 1950s; it now presents a well-developed body of theory and seems to be moving more slowly. By contrast, there is more research activity in the application of algebraic topology to problems arising elsewhere. The primary sources in these areas are papers in the learned journals, and these can be located in the usual way via Mathematical Reviews and similar bibliographical works. Of particular use here are the Reviews of papers in algebraic and differential topology, topological groups and homological algebra, edited by N.E. Steenrod, and published in two volumes by the American Mathematical Society, Providence, R.I. (1968).