2003/04/21 by Peter Teichner
Mathematics · #math.GT #msc:57M25 #msc:57N70 #msc:46L89
published as Proceedings of the ICM, Beijing 2002, vol. 2, 437--446
arxiv created 2003/04/21 · arxiv updated 2009/11/30
We explain new developments in classical knot theory in 3 and 4~dimensions, i.e. we study knots in 3-space, up to isotopy as well as up to concordance. In dimension~3 we give a geometric interpretation of the Kontsevich integral (joint with Jim Conant), and in dimension 4 we introduce new concordance invariants using von Neumann signatures (joint with Tim Cochran and Kent Orr). The common geometric feature of our results is the notion of a grope cobordism.