Self-referential discs and the light bulb lemma

Research output: Contribution to journalArticlepeer-review

Abstract

We show how self-referential discs in 4-manifolds lead to the construction of pairs of discs with a common geometrically dual sphere which are homotopic rel ∂, concordant and coincide near their boundaries, yet are not properly isotopic. This occurs in manifolds without 2-torsion in their fundamental group, e.g. the boundary connect sum of S2 × D2 and S1 × B3, thereby exhibiting phenomena not seen with spheres. On the other hand we show that two such discs are isotopic rel ∂ if the manifold is simply connected. We construct in S2 × D2 S1 × B3 a properly embedded 3-ball properly homotopic to a z0 × B3 but not properly isotopic to z0 × B3.

Original languageEnglish (US)
Pages (from-to)483-513
Number of pages31
JournalCommentarii Mathematici Helvetici
Volume96
Issue number3
DOIs
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • 4-manifold
  • Disc
  • Light bulb

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