Duality theorems in topology

Abstract

The present chapter is devoted to the early work on duality phenomena in topology. Of course, topology is a field which emerged from geometry during the 19th century, and we will see that there are rather explicit ties between the duality phenomena in question and classical duality in geometry. As is well known, a major step towards the development of topology as an independent mathematical subdiscipline in its present form was the work of Henri Poincare (1854-1912) on what he called “Analysis situs”; thus, it comes as no great surprise that the first duality studied in this context occurred in Poincare’s work and actually was the phenomenon later called Poincare duality.