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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The 4-dimensional light bulb theorem
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by David Gabai HTML | PDF
J. Amer. Math. Soc. 33 (2020), 609-652


For embedded 2-spheres in a 4-manifold sharing the same embedded transverse sphere homotopy implies isotopy, provided the ambient 4-manifold has no $\mathbb {Z}_2$-torsion in the fundamental group. This gives a generalization of the classical light bulb trick to 4-dimensions, the uniqueness of spanning discs for a simple closed curve in $S^4$ and $\pi _0(Diff_0(S^2\times D^2)/Diff_0(B^4))=1$. In manifolds with $\mathbb {Z}_2$-torsion, one surface can be put into a normal form relative to the other.
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Additional Information
  • David Gabai
  • Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
  • MR Author ID: 195365
  • Email:
  • Received by editor(s): July 14, 2017
  • Received by editor(s) in revised form: July 15, 2018, December 21, 2018, and January 31, 2019
  • Published electronically: June 15, 2020
  • Additional Notes: This research was partially supported by NSF grants DMS-1006553, 1607374
  • © Copyright 2020 David Gabai
  • Journal: J. Amer. Math. Soc. 33 (2020), 609-652
  • MSC (2000): Primary 57N13, 57N35
  • DOI:
  • MathSciNet review: 4127900