Jacobi identities in low-dimensional topology
几何拓扑
2012-02-21 v2
摘要
The Jacobi identity is the key relation in the definition of a Lie algebra. In the last decade, it also appeared at the heart of the theory of finite type invariants of knots, links and 3-manifolds (and is there called the IHX-relation). In addition, this relation was recently found to arise naturally in a theory of embedding obstructions for 2-spheres in 4-manifolds. We expose the underlying topological unity between the 3- and 4-dimensional IHX-relations, deriving from a picture of the Borromean rings embedded on the boundary of an unknotted genus three handlebody in 3-space. This is most naturally related to knot and 3-manifold invariants via the theory of grope cobordisms.
引用
@article{arxiv.math/0401427,
title = {Jacobi identities in low-dimensional topology},
author = {James Conant and Rob Schneiderman and Peter Teichner},
journal= {arXiv preprint arXiv:math/0401427},
year = {2012}
}
备注
Now closely approximates published version