This volume introduces the topology subseries of the EMS (there is a separate subseries on general topology). The author has collected the most important results of modern topology together with the motivating examples and applications, with a particular emphasis on geometry. Besides graduate students in topology, geometers and theoretical physicists at an advanced level should also find EMS 12 useful.

This up-to-date survey of the whole field of topology is the flagship of the topology subseries of the Encyclopaedia. The book gives an overview of various subfields, beginning with the elements and proceeding right up to the present frontiers of research.