ENGEL RELATIONS in 4-MANIFOLD TOPOLOGY

Michael Freedman, Vyacheslav Krushkal

Research output: Contribution to journalArticlepeer-review

Abstract

We give two applications of the 2-Engel relation, classically studied in finite and Lie groups, to the 4-dimensional (4D) topological surgery conjecture. The A-B slice problem, a reformulation of the surgery conjecture for free groups, is shown to admit a homotopy solution. We also exhibit a new collection of universal surgery problems, defined using ramifications of homotopically trivial links. More generally we show how n-Engel relations arise from higher-order double points of surfaces in 4-space.

Original languageEnglish
Article numbere22
JournalForum of Mathematics, Sigma
Volume4
DOIs
StatePublished - 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© The Author(s) 2016.

ASJC Scopus subject areas

  • Analysis
  • Theoretical Computer Science
  • Algebra and Number Theory
  • Statistics and Probability
  • Mathematical Physics
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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