Engel groups and universal surgery models
Geometric Topology
2021-09-30 v1
Abstract
We introduce a collection of 1/2--null 4-dimensional surgery problems. This is an intermediate notion between the classically studied universal surgery models and the -null kernels which are known to admit a solution in the topological category. Using geometric applications of the group-theoretic 2-Engel relation, we show that the 1/2--null surgery problems are universal, in the sense that solving them is equivalent to establishing 4-dimensional topological surgery for all fundamental groups. As another application of these methods, we formulate a weaker version of the -null disk lemma and show that it is sufficient for proofs of topological surgery and s-cobordism theorems for good groups.
Keywords
Cite
@article{arxiv.1707.07800,
title = {Engel groups and universal surgery models},
author = {Michael Freedman and Vyacheslav Krushkal},
journal= {arXiv preprint arXiv:1707.07800},
year = {2021}
}