Self-referential discs and the light bulb lemma

  • David Gabai

    Princeton University, USA
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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 and , 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 a properly embedded 3-ball properly homotopic to a but not properly isotopic to .

Cite this article

David Gabai, Self-referential discs and the light bulb lemma. Comment. Math. Helv. 96 (2021), no. 3, pp. 483–513

DOI 10.4171/CMH/518