Engel groups and universal surgery models

Michael Freedman, Vyacheslav Krushkal

Research output: Contribution to journalArticlepeer-review


We introduce a collection of (Formula presented.) - (Formula presented.) -null four-dimensional surgery problems. This is an intermediate notion between the classically studied universal surgery models and the (Formula presented.) -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 (Formula presented.) - (Formula presented.) -null surgery problems are universal, in the sense that solving them is equivalent to establishing four-dimensional topological surgery for all fundamental groups. As another application of these methods, we formulate a weaker version of the (Formula presented.) -null disk lemma and show that it is sufficient for proofs of topological surgery and s-cobordism theorems for good groups.

Original languageEnglish
Pages (from-to)1302-1316
Number of pages15
JournalJournal of Topology
Issue number3
StatePublished - 1 Sep 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2020 The Authors. Journal of Topology is copyright © London Mathematical Society.


  • 20F45
  • 57M25 (secondary)
  • 57N13 (primary)

ASJC Scopus subject areas

  • Geometry and Topology


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