2003/04/21 by Burt Totaro · 1 citation
Mathematics · #math.AG #msc:14F43 #msc:32S35 #msc:58J26
published as Proceedings of the ICM, Beijing 2002, vol. 2, 533--544
arxiv created 2003/04/21 · arxiv updated 2009/11/30
I will discuss recent progress by many people in the program of extending natural topological invariants from manifolds to singular spaces. Intersection homology theory and mixed Hodge theory are model examples of such invariants. The past 20 years have seen a series of new invariants, partly inspired by string theory, such as motivic integration and the elliptic genus of a singular variety. These theories are not defined in a topological way, but there are intriguing hints of their topological significance.