Engel groups and universal surgery models

Freedman M, Krushkal V. Engel groups and universal surgery models. J. Topol. 13 (2020), no. 3, 1302-1316. 2020.


We introduce a collection of 1/2-π1-null 4-dimensional surgery problems. This is an intermediate notion between the classically studied universal surgery models and the π1-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-π1-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 π1-null disk lemma and show that it is sufficient for proofs of topological surgery and s-cobordism theorems for good groups.

Last updated on 12/12/2023