Knots, von Neumann signatures, and grope cobordism
Geometric Topology
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0304299,
title = {Knots, von Neumann signatures, and grope cobordism},
author = {Peter Teichner},
journal= {arXiv preprint arXiv:math/0304299},
year = {2007}
}